Graph Theory Concepts Research Articles

Application of practice-based learning in graph theory

Learning graph theory is an important topic in the world of mathematics and computer science. However, students often face difficulties in understanding the concepts and practical application of graph theory. Therefore, this study aims to apply practicum-based learning methods in teaching graph theory to students. The method used in this study involves the application of practical work through the use of maple. Students are given the opportunity to interactively run experiments, analyze results, and relate them to graph theory concepts. Apart from that, they are also given assignments that focus on the practical application of graph theory in real-world contexts. This research was conducted on students of the Mathematics Education Study Program IKIP PGRI Pontianak, totaling 1 class using an experimental approach. The collected data were analyzed quantitatively to evaluate the effectiveness of practicum-based learning methods in increasing students' understanding of graph theory. The results of the study show that the application of practicum-based learning in graph theory has a positive impact on student understanding. Students show a significant increase in their understanding of graph theory concepts and their ability to apply the theory to real-world situations. In addition, students also provide positive feedback regarding interactive and fun learning experiences.

An Analysis of The Effect of Heterogeneously Distributed Inertia Constant in Generation Mix Power System by Using the Graph Theory and Dijkstra’s Algorithm

A modern power system with a generation mix of conventional and renewable energy sources (RES) creates stability issues. This requires a detailed analysis of the system with an exact share of active power through the generating sources according to nature, location, and control. The interconnected network with a large number of rotating machines at the generation side works coherently with each other. As the share of RES increases, it leads to reduce rotational inertia in the power system. The most important factor affected by inertia is the rate of change of frequency (RoCoF). The higher RoCoF leads the system more vulnerable to small disturbances in the power system. In a large power system network with numerous generating sources and transmission lines, it is difficult to determine the availability of inertia in the system. This paper incorporates the concept of graph theory in the IEEE 30 bus system to analyze the impact of heterogenous inertia distribution on frequency stability. The graph theory network gives the idea about the distance between the nodes and it is helpful to find the share of power from the generating sources. In this paper, we calculate the shortest path between the nodes or substations by using Dijkstra's algorithm. The betweenness centrality of the node detects the vulnerable nodes in the system from the frequency response point of view.

The average order of a connected induced subgraph of a graph and union‐intersection systems

AbstractBecause connectivity is such a basic concept in graph theory, extremal problems concerning the average order of the connected induced subgraphs of a graph have been of notable interest. A particularly resistant open problem is whether or not, for a connected graph of order , all of whose vertices have degree at least 3, this average is at least . It is shown in this paper that if is a connected, vertex transitive graph, then the average order of the connected induced subgraphs of is at least .The extremal graph theory problems mentioned above lead to a broader theory. The concept of a Union‐Intersection System (UIS) is introduced, being a finite set of points and a set of subsets of called blocks satisfying the following simple property for all : if , then . To generalize results on the average order of a connected induced subgraph of a graph, it is conjectured that if a UIS is, in various senses, “connected and regular,” then the average size of a block is at least half the number of points. We prove that if a union‐intersection set system is regular, completely irreducible, and nonredundant, then the average size of a block is at least half the number of points.

An Approach for Exploring Practical Phenomena In Social Network Analysis

Social networks like Facebook, LinkedIn, Twitter, WhatsApp, etc. have appeared more often these days, and their importance and influence in human life are growing rapidly. A social network is useful for connecting people to communicate and share information with one another in a virtual setting. A member of a social network can establish relationships with individual members or groups of members in that network. Utilizing networks and graph theory to construct social structures is the process known as social network analysis (SNA). The mapping and measurement of relationships and flows between individuals, groups, organizations, and so on is known as social network analysis (SNA). Social networks are represented using the concept of graph theory, where members of a social network are represented as nodes, and relationships between members are represented by edges, representing links, connections, and so on. The nodes represent the members of the social network, and the relationships between them are formed by the concept that there is either a direct or indirect path between them. Generally, members of social networks can establish relationships with each other using a one-to-one or one-to-many concept. The manner in which two or more members of a social network communicate or act toward one another constitutes relationships. The representation of social networks using graph theory helps to understand the trends in research on the relationships between different types of nodes and to predict the behaviour of nodes in social network analysis. The natural process of learning by doing is the subject of a subfield of computer science called machine learning (ML). ML assists in identifying patterns and the structure of node-to-node relationships in social networks. This paper attempts to study relationships among members of social networks using mathematical graph theory and machine learning.

OPTIMIZING SIMILARITY THRESHOLD FOR ABSTRACT SIMILARITY METRIC IN SPEECH DIARIZATION SYSTEMS: A MATHEMATICAL FORMULATION

Speaker diarization is a critical task in speech processing that aims to identify "who spoke when?" in an audio or video recording that contains unknown amounts of speech from unknown speakers and unknown number of speakers. Diarization has numerous applications in speech recognition, speaker identification, and automatic captioning. Supervised and unsupervised algorithms are used to address speaker diarization problems, but providing exhaustive labeling for the training dataset can become costly in supervised learning, while accuracy can be compromised when using unsupervised approaches. This paper presents a novel approach to speaker diarization, which defines loosely labeled data and employs x-vector embedding and a formalized approach for threshold searching with a given abstract similarity metric to cluster temporal segments into unique user segments. The proposed algorithm uses concepts of graph theory, matrix algebra, and genetic algorithm to formulate and solve the optimization problem. Additionally, the algorithm is applied to English, Spanish, and Chinese audios, and the performance is evaluated using wellknown similarity metrics. The results demonstrate that the robustness of the proposed approach. The findings of this research have significant implications for speech processing, speaker identification including those with tonal differences. The proposed method offers a practical and efficient solution for speaker diarization in real-world scenarios where there are labeling time and cost constraints

Block Encryption and Decryption of a Sentence Using Decomposition of the Turan Graph

Encryption and decryption are the two processes in cryptography to conceal and convey important information to an authorized person without third-party interruption in a network. Cryptography is a branch of computer science in which the system has to be updated every second. It mainly depends on mathematical concepts like number theory and algebra. Recently, graph theory concepts are employed in cryptography to make it stronger. The usage of complex graphs in cryptosystems makes it difficult to hack. In this paper, we proposed a cryptosystem using the Turan graph which has a complex graph structure. The advantage of using a Turan graph is that it is a unique multipartite complete graph with more edges than other multipartite complete graphs. This adds robustness to the cryptosystem. The novelty of this paper is the decomposition of the Turan graph into paths and stars and applying edge labeling to them to encrypt and decrypt a sentence of k words. The algorithms for encryption and decryption are also proposed in this paper.

On the Dominant Local Resolving Set of Vertex Amalgamation Graphs

Basically, the new topic of the dominant local metric dimension which be symbolized by Ddim_l (H) is a combination of two concepts in graph theory, they were called the local metric dimension and dominating set. There are some terms in this topic that is dominant local resolving set and dominant local basis. An ordered subset W_l is said a dominant local resolving set of G if W_l is dominating set and also local resolving set of G. While dominant local basis is a dominant local resolving set with minimum cardinality. This study uses literature study method by observing the local metric dimension and dominating number before detecting the dominant local metric dimension of the graphs. After obtaining some new results, the purpose of this research is how the dominant local metric dimension of vertex amalgamation product graphs. Some special graphs that be used are star, friendship, complete graph and complete bipartite graph. Based on all observation results, it can be said that the dominant local metric dimension for any vertex amalgamation product graph depends on the dominant local metric dimension of the copied graphs and how the terminal vertex is constructed

Pendampingan UMKM Penjahit Berbasis Teknologi Digital dalam Perspektif Industri Kreatif di Bogor Utara

Tailoring Micro, Small and Medium Enterprises (MSMEs) or often called Tailors experienced an extraordinary economic downturn during the Covid-19 pandemic. Convection innovation as a form of existence in the midst of a pandemic outbreak that still exists today to survive must carry out various kinds of creativity. One of them is digitizing the marketing system, updating fashion trends, increasing relationships, providing the best service, collaborating with agencies, and others. In this service the focus is on digitizing the system and developing the concept of relations using the graph theory concept to increase competitiveness. The location of the service will be focused on one of the tailors, namely Sarinah Tailor in Kedunghalang Village, North Bogor District.

Graph Theory in DNA Sequencing: Unveiling Genetic Patterns

Graph theory, a branch of mathematics that studies the properties and relationships of graphs, has emerged as a powerful tool in addressing the complexities of DNA sequencing. This paper highlights the application of graph theory in DNA sequencing and its implications in various aspects of genomics research. One fundamental concept in graph theory applied to DNA sequencing is the construction of the de Bruijn graph. This graph represents overlapping k-mers, subsequences of length k, as nodes, with edges connecting adjacent k-mers. By constructing and analyzing the de Bruijn graph, researchers can infer the underlying DNA sequence, detect errors, resolve repetitive regions, and identify structural variations in the genome. Graph algorithms such as Overlap path, Eulerian path and Hamiltonian path have been adapted to reconstruct complete DNA sequences from fragmented reads obtained through sequencing. These algorithms leverage the connectivity information present in the de Bruijn graph to traverse and assemble the reads, enabling the reconstruction of long DNA sequences accurately. the application of graph theory in DNA sequencing has revolutionized the field of genomics by providing powerful computational tools for DNA assembly, sequence analysis, and functional annotation. By leveraging graph theory concepts and algorithms, researchers can unravel the intricate information embedded within DNA sequences, leading to deeper insights into the genetic basis of life and its applications in various fields, including medicine, agriculture, and evolutionary biology. Future developments in graph-based algorithms and computational techniques hold promise for further enhancing our ability to unlock the secrets encoded within the vast realm of DNA sequences.

Sierpinski Graflarının Tepe-Ayrıt Temelli Derece Özellikleri Üzerine

Network science and graph theory are two important branches of mathematics and computer science. Many problems in engineering and physics are modeled with networks and graphs. Topological analysis of networks enable researchers to analyse networks in relation some physical and engineering properties without conducting expensive experimental studies. Topological indices are numerical descriptors which defined by using degree, distance and eigen-value notions in any graph. Most of the topological indices are defined as by using classical degree concept in graph theory, network and computer science. Recently two novel degree parameters have been defined in graph theory: Vertex-edge degree and Edge-vertex degree. Vertex-edge degree and edge-vertex degree based topological indices have been defined as parallel to their corresponding classical degree counterparts. Generalized Sierpinski networks have an important place of applications in view of engineering science especially in computer science. Classical degree based topological properties of generalized Sierpinski graphs have been investigated by many studies. In this article, vertex-edge degree based topological indices values of generalized Sierpinski graphs have been computed.

On physical analysis of free Gibb’s energy based on topological indices for nickel sulfide

Nickel sulfides are inorganic compounds of chalcogens and transition metals with formula of NiSx, where nickel is from 10th group and sulfur is from 16th group of periodic table. Topological indices play a key role in analyzing and understanding the topology of chemical compounds. In the chemical structure of any compound, atoms are considered as vertices, while the bounds between these atoms are edges. The purpose of this paper is to analyses the structure of nickel (II) sulfide. Moreover, we have computed the topological indices of molecular structure of nickel (II) sulfide. The regression models between the standard molar free Gibb’s energy, specific heat and each topological index of nickel (II) sulfide for different formula units have been developed. The basic purpose of these regression models is to develop a relationship between free Gibb’s energy GE, specific heat Cp and topological indices of nickel (II) sulfide. More preciously, we provided a new direction in this field of research to analysis the physio-chemical properties like Gibb’s energy using the concept of chemical graph theory.

Generation of Synthetic Water Distribution Data Using a Multiscale Generator-Optimizer

Rare or limited access to real-world data has widely been a stumbling block for the development and employment of design optimization and simulation models in water distribution systems (WDS). Primary reasons for such accessibility issues could include data unavailability and high security protocols. Synthetic data can play a major role as a reliable alternative to mimic and replicate real-world WDS for modeling purposes. This study puts forth a comprehensive approach to generate synthetic WDS infrastructural data by (1) employing graph-theory concepts to generate multitudinous WDS skeleton layouts through retaining the critical topological features of a given real WDS; and (2) assigning component sizes and operational features such as nodal demands, pump curves, pipe sizes, and tank elevations to the generated WDS skeleton layouts through a multiobjective genetic algorithm (GA)–based design optimization scheme. Thousands of such generated-optimized networks are statistically analyzed in terms of the fundamental WDS characteristics both collectively and granularly. An outstanding novelty in this study includes an automatedly integrated algorithmic function that attempts to (1) simultaneously optimize the generated network in a biobjective scheme, (2) rectify pipe intersections that violate pipeline embedding standards, and (3) correct the unusual triangular loops in the generator by honoring the conventional square-shaped loop connectivity in a WDS. The proposed modeling approach was demonstrated in this study using the popular Anytown water distribution benchmark system. Generation and optimization of such representative synthetic networks pave the way for extensive access to representative case-study models for academic and industrial purposes while the security of the real-world infrastructure data is not compromised.

Applications of Mathematical in Computer Science

Abstract: Mathematics (The QUEEN’s mother of all Sciences), is the foundation of Computer Science. Mathematics can be perceived in our garden or park from symmetry of leaves, flowers, fruits etc. and by so many examples of Geometry and symmetry can be seen in nature. Scientists and researchers cannot ideally accomplish their work without the inclusion of mathematics. Mathematics is sociable for analytical skills needed in Computer Disciplines like; Concepts of binary number system, Boolean algebra, Calculus, Discrete mathematics, linear algebra, number theory, and graph theory are the most applicable to the subject of computer science with the accessional emergence of new concepts like machine learning, artificial intelligence, virtual reality and augmented reality make the future of mathematics grow endless. Mathematics has been an important intellectual preoccupation of man for a long time. Computer Science as a formal discipline is about seven decades young. Is the almost spontaneous use of computing? In this article, this paper convey to the frontage the many close connections and parallels between the Mother and daughter sciences. The paper underscores the strong interplay and interactions by looking at some exciting contemporary results from number theory and combinatorial mathematics and algorithms of computer science.

On Divided-Type Connectivity of Graphs

The graph connectivity is a fundamental concept in graph theory. In particular, it plays a vital role in applications related to the modern interconnection graphs, e.g., it can be used to measure the vulnerability of the corresponding graph, and is an important metric for reliability and fault tolerance of the graph. Here, firstly, we introduce two types of divided operations, named vertex-divided operation and edge-divided operation, respectively, as well as their inverse operations vertex-coincident operation and edge-coincident operation, to find some methods for splitting vertices of graphs. Secondly, we define a new connectivity, which can be referred to as divided connectivity, which differs from traditional connectivity, and present an equivalence relationship between traditional connectivity and our divided connectivity. Afterwards, we explore the structures of graphs based on the vertex-divided connectivity. Then, as an application of our divided operations, we show some necessary and sufficient conditions for a graph to be an Euler's graph. Finally, we propose some valuable and meaningful problems for further research.

A Graph Theory Based Self-Learning Honeypot to Detect Persistent Threats

Attacks on the cyber space is getting exponential in recent times. Illegal penetrations and breaches are real threats to the individuals and organizations. Conventional security systems are good enough to detect the known threats but when it comes to Advanced Persistent Threats (APTs) they fails. These APTs are targeted, more sophisticated and very persistent and incorporates lot of evasive techniques to bypass the existing defenses. Hence, there is a need for an effective defense system that can achieve a complete reliance of security. To address the above-mentioned issues, this paper proposes a novel honeypot system that tracks the anonymous behavior of the APT threats. The key idea of honeypot leverages the concepts of graph theory to detect such targeted attacks. The proposed honeypot is self-realizing, strategic assisted which withholds the APTs actionable techniques and observes the behavior for analysis and modelling. The proposed graph theory based self learning honeypot using the results γ(C(n,1)),γc (C(n,1)), γsc (C(n,1)) outperforms traditional techniques by detecting APTs behavioral with detection rate of 96%.

Malicious Activities Prediction Over Online Social Networking Using Ensemble Model

With the vast advancements in Information Technology, the emergence of Online Social Networking (OSN) has also hit its peak and captured the attention of the young generation people. The clone intends to replicate the users and inject massive malicious activities that pose a crucial security threat to the original user. However, the attackers also target this height of OSN utilization, explicitly creating the clones of the user’s account. Various clone detection mechanisms are designed based on social-network activities. For instance, monitoring the occurrence of clone edges is done to restrict the generation of clone activities. However, this assumption is unsuitable for a real-time environment and works optimally during the simulation process. This research concentrates on modeling and efficient clone prediction and avoidance methods to help the social network activists and the victims enhance the clone prediction accuracy. This model does not rely on assumptions. Here, an ensemble Adaptive Random Subspace is used for classifying the clone victims with k-Nearest Neighbour (k-NN) as a base classifier. The weighted clone nodes are analysed using the weighted graph theory concept based on the classified results. When the weighted node’s threshold value is higher, the trust establishment is terminated, and the clones are ranked and sorted in the higher place for termination. Thus, the victims are alert to the clone propagation over the online social networking end, and the validation is done using the MATLAB 2020a simulation environment. The model shows a better trade-off than existing approaches like Random Forest (RF), Naïve Bayes (NB), and the standard graph model. Various performance metrics like True Positive Rate (TPR), False Alarm Rate (FAR), Recall, Precision, F-measure, and ROC and run time analysis are evaluated to show the significance of the model.

Social Network Analysis to Examine the Effectiveness of e-PBL with Design Thinking to Foster Collaboration: Comparisons between High and Low Self-regulated Learners

In TVET teaching and learning, learners’ collaboration is important to ensure learning effectiveness. However, employing either design thinking or online problem-based learning would not lead to fruitarian. Hence, to devise teaching and learning that employs design thinking (DT) and online problem-based learning (ePBL) pedagogies used in tandem with social media learning environment in Facebook are hypothesized to improve TVET learner’s collaboration. By adopting the Social Constructivism learning theory that social interaction fosters collaborative learning and build learners’ knowledge and understanding, this study is commenced. Social interaction that fosters learners’ collaboration is moderated by type of learners’ self-regulation (SR) towards learning. Previous research hypothesized that ePBL alone only workedeffectively for high self-regulated learners. The learning outcome inequity present due to the pedagogy limitation. This research devises ePBL with DT as a combination of pedagogies that benefits the low SR learners as well. To monitor collaborative learning occurrences, network ties via social media footprints of individual TVET learners is tracked from the learners’ Facebook group. The effectiveness of treatments is monitored using social network analysis i.e. graph theory and centrality concept employing NodeXL software. Samples of 142 TVET pre-service teachers that currently enroll in Design and Technology course at Teachers’ Training Institutes in Malaysia participated in this study. The samples are intact group and classified into high-SR learners and low-SR learners. Social network analysis using Vertices index, Geodesic distance and graph visualization findings show that ePBL with DT works in fostering learning collaboration for both high-SR and low-SR learners. This implies that national e-learning policy and ePBL embeddedness into technical subject is promising, regardless of the type of learners provided that DT is incorporated into the pedagogy.

Engineering Nearly Linear-time Algorithms for Small Vertex Connectivity

Vertex connectivity is a well-studied concept in graph theory with numerous applications. A graph is k -connected if it remains connected after removing any k −1 vertices. The vertex connectivity of a graph is the maximum k such that the graph is k -connected. There is a long history of algorithmic development for efficiently computing vertex connectivity. Recently, two near linear-time algorithms for small k were introduced by Forster et al. [SODA 2020]. Prior to that, the best-known algorithm was one by Henzinger et al. [FOCS 1996] with quadratic running time when k is small. In this article, we study the practical performance of the algorithms by Forster et al. In addition, we introduce a new heuristic on a key subroutine called local cut detection, which we call degree counting. We prove that the new heuristic improves space-efficiency (which can be good for caching purposes) and allows the subroutine to terminate earlier. According to experimental results on random graphs with planted vertex cuts, random hyperbolic graphs, and real-world graphs with vertex connectivity between 4 and 8, the degree counting heuristic offers a factor of 2–4 speedup over the original non-degree counting version for small graphs and almost 20 times for some graphs with millions of edges. It also outperforms the previous state-of-the-art algorithm by Henzinger et al., even on relatively small graphs.

Spectral Data Analysis for Forgery Detection in Official Documents: A Network-Based Approach

Despite the huge advances in digital communications in the last decade, physical documents are still the most common media for information transfer, especially in the official context. However, the readily available document processing devices and techniques (printers, scanners, etc.) facilitate the illegal manipulation or imitation of original documents by forgers. Therefore, verification of the authenticity and detection of forgery is of paramount importance to all agencies receiving printed documents. We suggest an unsupervised forgery detection framework that can distinguish whether a document is forged based on the spectroscopy of the document’s ink. The spectra of the tested documents inks (original and questioned) were obtained using laser-induced breakdown spectroscopy (LIBS) technology. Then, a correlation matrix of the spectra was calculated for both the original and questioned documents together, which were then transformed into an adjacency matrix aiming at converting it into a weighted network under the concept of graph theory. Clustering algorithms were then applied to the network to determine the number of clusters. The proposed approach was tested under a variety of scenarios and different types of printers (e.g., inkjet, laser, and photocopiers) as well as different kinds of papers. The findings show that the proposed approach provided a high rate of accuracy in identifying forged documents and a high detection speed. It also provides a visual output that is easily interpretable to the non-expert, which provides great flexibility for real-world application.

An Approach of Graph Theory on Cryptography

Abstract: In this paper, we discuss about the connection between graph theory and cryptography. We use the spanning tree concept of graph theory to encryption the message