Conceptual Graphs Research Articles

On Domination and Related Concepts of Multidimensional Fuzzy Graphs and Their Applications

Domination and its associated concepts are significant ideas in fuzzy graph theory that have applications in diverse fields such as neural networks, game theory, and telecommunication. This study presents the notions of dominance and its associated research in a broader form of fuzzy graph called the multidimensional fuzzy graph. Basic results, such as the relationship between these parameters and vertices, edges, minimal sets, and so forth, are identified and illustrated with appropriate examples. The dominance number of multidimensional fuzzy graphs is determined after undergoing operations such as direct product, tensor product, composition, join, and others. Ultimately, this study displays a decision-making problem that can be efficiently addressed by utilizing the concept of the dominance number. The effectiveness of this approach is then compared to various models, like [Formula: see text]-polar fuzzy sets.

Towards Nash‐Williams orientation conjecture for infinite graphs

AbstractIn 1960 Nash‐Williams proved that an edge‐connectivity of is sufficient for a finite graph to have a ‐arc‐connected orientation. He then conjectured that the same is true for infinite graphs. In 2016, Thomassen, using his own results on the auxiliary lifting graph, proved that ‐edge‐connected infinite graphs admit a ‐arc‐connected orientation. Here we improve this result for the class of one‐ended locally finite graphs and show that an edge‐connectivity of is enough in that case. Crucial to this improvement are results presented in a separate paper, by the same author of this paper, on the key concept of the lifting graph, extending results by Ok, Richter, and Thomassen.

Novel Concepts of Bipolar Picture Fuzzy Graphs With Applications in Image Segmentation and Road Maps Designs

Novel Concepts of Bipolar Picture Fuzzy Graphs With Applications in Image Segmentation and Road Maps Designs

Properties of Cubic Fuzzy Competition Graphs with Applications

This study extends the concept of competition graphs to cubic fuzzy competition graphs by introducing additional variations including cubic fuzzy out-neighbourhoods, cubic fuzzy in-neighbourhoods, open neighbourhood cubic fuzzy graphs, closed neighbourhood cubic fuzzy graphs, cubic fuzzy (k) neighbourhood graphs and cubic fuzzy [k]-neighbourhood graphs. These variations provide further insights into the relationships and competition within the graph structure, each with its own defined characteristics and examples. These cubic fuzzy CMGs are further classified as cubic fuzzy k-competition graphs that show competition in the k th order between components, p -competition cubic fuzzy graphs that concentrate on competition in terms of membership degrees, and m -step cubic fuzzy competition graphs that analyze competition in terms of steps. Further, some related results about independent strong vertices and edges have been obtained for these cubic fuzzy competition graph classes. Finally, the proposed concept of cubic fuzzy competition graphs is supported by a numerical example. This example showcases how the framework of cubic fuzzy competition graphs can be practically applied to the predator-prey model to illustrate the representation and analysis of ambiguous information within the graph structures.

Overlapping Structure Detection in Protein-Protein Interaction Networks Using a Modified Version of Particle Swarm Optimization

In today's world, the science of bioinformatics is developing rapidly, especially with regard to the analysis and study of biological networks. Scientists have used various nature-inspired algorithms to find protein complexes in protein-protein interaction (PPI) networks. These networks help scientists guess the molecular function of unknown proteins and show how cells work regularly. It is very common in PPI networks for a protein to participate in multiple functions and belong to many complexes, and as a result, complexes may overlap in the PPI networks. However, developing an efficient and reliable method to address the problem of detecting overlapping protein complexes remains a challenge since it is considered a complex and hard optimization problem. One of the main difficulties in identifying overlapping protein complexes is the accuracy of the partitioning results. In order to accurately identify the overlapping structure of protein complexes, this paper has proposed an overlapping complex detection algorithm termed OCDPSO-Net, which is based on PSO-Net (a well-known modified version of the particle swarm optimization algorithm). The framework of the OCDPSO-Net method consists of three main steps, including an initialization strategy, a movement strategy for each particle, and enhancing search ability in order to expand the solution space. The proposed algorithm has employed the partition density concept for measuring the partitioning quality in PPI network complexes and tried to optimize the value of this quantity by applying the line graph concept of the original graph representing the protein interaction network. The OCDPSO-Net algorithm is applied to a Collins PPI network and the obtained results are compared with different state-of-the-art algorithms in terms of precision ( ), recall ( ), and F-measure ( ). Experimental results confirm that the proposed algorithm has good clustering performance and has outperformed most of the existing recent overlapping algorithms. .

Visualization and Analysis of Three-Way Data Using Accumulated Concept Graphs

This paper introduces the Accumulated Concept Graph (ACG), a visualization tool based on the quantile method designed to analyze three-way data, including distributional data. Such data often have complex structures that make it difficult to identify patterns using conventional visualization techniques. The ACG represents each object with one or more monotonic line graphs. As a result, the three-way data are visualized as a set of parallel monotonic line graphs that never intersect. This non-intersecting property allows for the easy identification of both macroscopic and microscopic patterns within the data. We demonstrate the usefulness of ACGs and principal component analysis in the analysis of real three-way datasets.

Fuzzy Outerplanar Graphs and Its Applications

The concept of a crisp graph is essential in the study of outerplanar graphs because outerplanar graphs are a unique type of planar graphs containing special characteristics. One of the core concepts of crisp graphs, the notion of a subgraph, is utilized primarily to solve difficult data problems. In this paper, researching outerplanar graphs in fuzzy graphs is the main aim of the work. By allowing edges connecting vertices to have varying levels of membership or fuzziness, a fuzzy graph is a mathematical framework that develops on the concept of crisp graphs. Because of their capacity to describe unclear or imprecise relationships between items, fuzzy outerplanar graphs might have potential applications. The subgraphs of fuzzy outerplanar graphs are revealed by eliminating specific vertices or edges from the fuzzy graphs. Furthermore, maximum, and maximal fuzzy outerplanar subgraphs defined for both vertex and edge deletion are examined using examples. Some of the connections between the concepts discussed are represented as theorems and conclusions. An application for the layout of a bypass road is discussed using the proposed concepts.

On the unit-Jacobson graph

In this paper, we introduce the unit-Jacobson graph, which is defined by the unit elements and the elements of the Jacobson radical of a commutative ring [Formula: see text] with nonzero identity. We give relationships between this new graph concept and some special rings such as [Formula: see text]-clean rings, [Formula: see text]-rings, local rings, and cartesian rings. Moreover, we investigate the concepts of the dominating set, diameter, and girth on the unit-Jacobson graph.

Concept graph embedding models for enhanced accuracy and interpretability

Concept graph embedding models for enhanced accuracy and interpretability

Hurwitz enumeration problem through the perspective of Cayley graph

The Hurwitz enumeration problem studies how to determine the Hurwitz number for a branch profile, which counts the number of ways a per mutation can be factored into transpositions. In this paper, we consider the length of strictly monotone factorization from the perspective of Cayley graph theory. We represent the factorization problem using a Cayley graph, where vertices are permutations and edges are transpositions. Our focus is proving the unique monotone factorization theorem, which states that for a given permutation, there is only one monotone factorization of minimal length. To prove this, we employ inductive arguments on the structure of the Cayley graph. The key insight is using the connectivity of the graph and properties of shortest paths to characterize the uniqueness of the minimal factorization. This inductive approach allows us to rigorously connect the combinatorial Hurwitz problem to foundational graph concepts. Overall, this paper makes important theoretical advances in enumerating Hurwitz numbers by using Cayley graphs and induction to prove the novel unique monotone factorization theorem. The connections drawn between combinatorics, graphs, and inductive proofs are technically innovative. This theoretical foundation will hopefully stimulate further research into the deep links between the Hurwitz problem and other branches of mathematics.

Some New Concepts of Interval-Valued Picture Fuzzy Graphs and Their Application Toward the Selection Criteria

Some New Concepts of Interval-Valued Picture Fuzzy Graphs and Their Application Toward the Selection Criteria

Towards Modeling Conceptual Graphs and Transparent Intensional Logic

Towards Modeling Conceptual Graphs and Transparent Intensional Logic

Embedding of Neutrosophic Graphs on Topological Surfaces

Background: A planar graph (PG) is a graph with no intersecting edges. Particular to both crisp and neutrosophic graphs (NG) is the planar graph, in contrast to crisp planar graphs. NPGs allow for the intersection of neutrosophic edge NEs, since the value of planarity in these graphs is the degree of planarity of the intersected NEs. The NPGs are often represented on a flat surface. Materials and Methods: This study discusses how to embed NGs on surfaces such as spheres and m-toruses by defining the degree of intersection of the neutrosophic edges of NGs with finding the faces on the given graph structures using Euler's theorems. Here, the proofs of Euler's theorems help us find, given the total NFV of G, the interval containing that value. Result: As result of this work obtained that for any two isomorphic planer graphs, they have the same planarity value. For any neutrosophic planer graph with f = (1,1,1) can be embedded in the plane if it can be embedded in the sphere and according to NPGs, for planar and spherical surfaces, equivalent theorems to Euler's formula are proved and shown. Conclusion: It concludes that by using neutrosophic sets and crisp graphs to construct neutrosophic graphs with the benefit of Euler’s theorem, it can provide the concept of embedding neutrosophic graphs in different topological surfaces such as a plane, sphere, and m-torus.

On some operations on grey graphs with application

PurposeThe objective of this paper is to formulate the precise meanings of grey graphs and examine some of their properties.Design/methodology/approachThis article introduces innovative concepts of grey sets based on the grey number. We establish the grey graphs and examine their essential properties as isomorphisms of these graphs. Additionally, we explore the notion of a grey-complete graph and demonstrate certain properties of self-complementary grey-complete graphs.FindingsWe showcase novel facets of grey system theory through the establishment of the structures of grey graphs, and the subsequent analysis of their distinctive traits.Practical implicationsThis article provides us with a new theoretical direction for grey system theory according to grey numbers. Thus, we present test examples that explain the routes between cities and the electrical wires between homes. Furthermore, the concept of grey graphs can be applied in several areas of engineering, computer science, neural networks, artificial intelligence, and medical diagnosis.Originality/valueThe proposed concepts are considered novel mathematical directions in grey system theory for the first time. Some operations of grey graphs are also explored.

Comparative study of two Soft Graph Concepts

Comparative study of two Soft Graph Concepts

Concept graph construction and applied research of agricultural remote sensing

ABSTRACT Remote sensing technology in the new era gradually need a new scientific paradigm driven by big data and knowledge. However, in the current research, the use of existing knowledge is slightly insufficient. As for the whole research process, there is a lack of guidance based on the field knowledge. In view of the above problems in the field of remote sensing in agriculture, it is of great significance to organize knowledge based on concept graph and develop knowledge-driven big data analysis theory and methods. This paper focuses on the construction and application of agricultural remote sensing concept graph. Firstly, it explores the core contents, research hotspots and development trends of the current agricultural remote sensing field through reference visualization and analysis methods such as keyword frequency statistics, keyword co-occurrence, word detection with stronger citation burst and so on. Then, this paper summarizes the comprehensive ontology of agricultural remote sensing based on the results of keyword clustering. Thus, the schema layer of concept graph is constructed from top to bottom. Under the guidance of the schema layer, the data layer of the concept graph is artificially filled from the bottom up with different triads stored in Neo4j. In terms of application, retrieval, query and recommendation of the proposed concept graph for agricultural remote sensing tasks is a typical application case. Based on the results of the recommendation, it could guide the process of information extraction such as cultivated land parcel delineation and crop type identification at the parcel scale. The study of concept graph helps to summarize and generalize the relevant knowledge in the field of agricultural remote sensing. Relevant research provide effective solutions for automated and intelligent agricultural information extraction and application.

A study on deg-centric graphs

The deg-centric graph of a simple, connected graph G, denoted by Gd, is a graph constructed from G such that, V(Gd) = V(G) and E(Gd) = {vivj: dG(vi,vj) ≤ degG(vi)}. In this paper, the concepts of deg-centric graphs and iterated deg-centrication of a graph are introduced and discussed.

Induced dominating sequence and ESD graphs

A vertex subset D of a graph G = (V,E) is said to be a dominating set if every vertex in G is either in D or adjacent to some vertex in D. The minimum cardinality of such a set is the domination number, which is denoted as γ(G). In this paper, we define a sequence associated with the domination concept in graphs and studied the basic properties of the sequence in terms of various parameters of graphs. Using this sequence we order the vertices of a dominating set according its significance and propose Equally Significant Dominating (ESD) graphs. We also introduced domination related topological indices and compute their lower bounds for trees, unicyclic graphs and bicyclic graphs. All the graphs attaining the bounds are characterized.

CONCEPT OF MICROBIOLOGICAL GRAPH OF FEED AND FOOD PRODUCTION

Compound feeds are favorable environments for microorganisms, namely bacteria and fungi. Both groups contain nonpathogenic, opportunistic and pathogenic members. Bacteria can cause infections, and fungi can cause mycotoxicoses, so controlling microbial contamination of feed is of great importance. Sources of microbial contamination of compound feed include both raw materials and the production environment: air, surfaces, equipment, and the hands and clothing of employees. As raw materials and pre-products move through production lines, they undergo certain processes that can either reduce or increase microbial contamination. The reducing processes include grain dehulling and high-temperature processing (moisture and heat treatment, conditioning, extrusion, expansion, drying of minerals, granulation), while the increasing processes include making preliminary mixtures, grinding, dosing and mixing, and the production of grits. In dosing and mixing, the contribution of each component is determined by its dose and has a two-way effect: the component contributes its microbiota, but its mass dilutes the mixture. The sequence of these processes represents a certain dynamics of microbial burden, which will result in the contamination level of the finished product lower or higher than in the initial raw material. This sequence can be represented as a microbiological graph, the vertices of which are the positive or negative contributions of the processes to the microbiological burden of the material. And the system of such vertices can be represented as a simple mathematical equation. Creating microbiological graphs for individual production lines or for the manufacture as a whole can help to understand the microbiological dynamics in a material or product and apply appropriate corrective measures to prevent microbiological hazards in the final product. This paper proposes a method of making a microbiological graph with two types of vertex designations for the IV generation compound feed production, as well as a mathematical apparatus for calculating the vertices of the graph.

Stock Trend Prediction with Machine Learning: Incorporating Inter-Stock Correlation Information through Laplacian Matrix

Predicting stock trends in financial markets is of significant importance to investors and portfolio managers. In addition to a stock’s historical price information, the correlation between that stock and others can also provide valuable information for forecasting future returns. Existing methods often fall short of straightforward and effective capture of the intricate interdependencies between stocks. In this research, we introduce the concept of a Laplacian correlation graph (LOG), designed to explicitly model the correlations in stock price changes as the edges of a graph. After constructing the LOG, we will build a machine learning model, such as a graph attention network (GAT), and incorporate the LOG into the loss term. This innovative loss term is designed to empower the neural network to learn and leverage price correlations among different stocks in a straightforward but effective manner. The advantage of a Laplacian matrix is that matrix operation form is more suitable for current machine learning frameworks, thus achieving high computational efficiency and simpler model representation. Experimental results demonstrate improvements across multiple evaluation metrics using our LOG. Incorporating our LOG into five base machine learning models consistently enhances their predictive performance. Furthermore, backtesting results reveal superior returns and information ratios, underscoring the practical implications of our approach for real-world investment decisions. Our study addresses the limitations of existing methods that miss the correlation between stocks or fail to model correlation in a simple and effective way, and the proposed LOG emerges as a promising tool for stock returns prediction, offering enhanced predictive accuracy and improved investment outcomes.