Part Of Graph Theory Research Articles

The Partition Dimension of a Path Graph

Resolving partition is part of graph theory. This article, explains about resolving partition of the path graph, with. Given a connected graph and is a subset of writen . Suppose there is , then the distance between and is denoted in the form . There is an ordered set of -partitions of, writen then the representation of with respect tois the The set of partitions ofis called a resolving partition if the representation of each to is different. The minimum cardinality of the solving-partition to is called the partition dimension of G which is denoted by . Before getting the partition dimension of a path graph, the first step is to look for resolving partition of the graph. Some resolving partitions of path graph, with , and are obtained. Then, the partition dimension of the path graph which is the minimum cardinality of resolving partition, namely pd (Pn)=2Resolving partition is part of graph theory. This article, explains about resolving partition of the path graph, with. Given a connected graph and is a subset of writen . Suppose there is , then the distance between and is denoted in the form . There is an ordered set of -partitions of, writen then the representation of with respect tois the The set of partitions ofis called a resolving partition if the representation of each to is different. The minimum cardinality of the solving-partition to is called the partition dimension of G which is denoted by . Before getting the partition dimension of a path graph, the first step is to look for resolving partition of the graph. Some resolving partitionsof path graph, with , and are obtained. Then, the partition dimension of the path graph which is the minimum cardinality of resolving partition, namely.

Application of Basic Graph Theory in Autonomous Motion of Robots

Discrete mathematics covers the field of graph theory, which solves various problems in graphs using algorithms, such as coloring graphs. Part of graph theory is focused on algorithms that solve the passage through mazes and labyrinths. This paper presents a study conducted as part of a university course focused on graph theory. The course addressed the problem of high student failure in the mazes and labyrinths chapter. Students’ theoretical knowledge and practical skills in solving algorithms in the maze were low. Therefore, the use of educational robots and their involvement in the teaching of subjects in part focused on mazes and labyrinths. This study shows an easy passage through the individual areas of teaching the science, technology, engineering, and mathematics (STEM) concept. In this article, we describe the research survey and focus on the description and examples of teaching in a university course. Part of the work is the introduction of an easy transition from the theoretical solution of algorithms to their practical implementation on a real autonomous robot. The theoretical part of the course introduced the issues of graph theory and basic algorithms for solving the passage through the labyrinth. The contribution of this study is a change in the approach to teaching graph theory and a greater interconnection of individual areas of STEM to achieve better learning outcomes for science students.

Facebook or fail-book: Exploring “community” in a virtual community of practice

AbstractCreating collaborative working and learning experiences has long been at the forefront of computer-assisted language learning research. It is in this context that, in recent years, the integration of social networking sites and Web 2.0 in learning settings has surged, generating new opportunities to establish and explore virtual communities of practice (VCoPs). However, despite the number of studies on the concept, research remains inconclusive on how learners develop a sense of community in a VCoP, and what effect this may have on interaction and learning. This research project proposes to use social network analysis, part of graph theory, to explore the configuration of a set of VCoPs, and presents an empirical approach to determine how interaction in such communities takes shape. The present paper studies the concept of “community” in two VCoPs on Facebook. Participants (Group 1: N = 123, Group 2: N = 34) in both VCoPs are enrolled in English as a foreign language courses at two Belgian institutions of higher education. Social network analysis is used to show how both learner groups establish and develop a network of peers, and how different participants in those groups adopt different roles. Participation matrices reveal that interaction mainly revolves around a number of active key figures and that certain factors such as the incorporation of online and offline assignments and the inclusion of a teacher online result in varying levels of success when establishing collaborative dialogue within the VCoPs. Recommendations are formulated to inform and improve future practice.

DIMENSI PARTISI GRAF LENGKAP

Resolving partition is part of graph theory. Resolving partition is needed to obtain partition dimension. So far it has not been discussed regarding resolving partition of complete graphs. For this reason, this article explains the resolving partition of a complete graph.Given a connected graph and is a subset of write . Suppose there is then the distance between to is denoted in the form of . Then, suppose there is a partitioned set of , write , then we can obtain a representation of in the form of The partition set is called a resolving partition if the representation of each ∈ with is different. The minimum cardinality of the resolving -partition against is called the partition dimension of , denoted by pd (). To get the partition dimension of a complete graph, first we find the resolving partition og the graph, resolving partition orde After that, to assist in obtaining the partition dimensions of complete graph, we explained that if is is a connected graph then Based on these steps, finally obtained that the partition dimension of the complete graph, namely

Problem of Maximum Matching in Non-Bipartite Graph Using Edmonds’ Cardinality Matching Algorithm and Its Applicationin the Battle of Britain Case

Matching is a part of graph theory that discusses pair. A matching M is called to be maximum if M has the highest number of elements. A blossom which is encountered in non-bipartite graph can cause failure in process of finding the maximum matching in non-bipartite graph. One of the algorithms that can be used to find a maximum matching in non-bipartite graph is Edmonds’ Cardinality Matching Algorithm. Shrinking process is done in each blossom Bi that is encountered to become pseudovertex bi, in a way that each blossom does not interfere the process of finding a maximum matching in non-bipartite graph. In order to accelerate the finding, simple greedy method is used to perform initialization of matching and BFS algorithm is also used in constructing an alternating tree in a non-bipartite graph.The research discussed the finding of maximum matching in non-bipartite graph using Edmonds’ cardinality matching algorithm. In addition, this research gave a sample of its application in the resolution of The Battle of Britain case. The result obtained is a maximum matching in non-bipartite graph. The maximum matching obtained is a solution to the case of The Battle of Britain.

Topological Filtering of Dynamic Functional Brain Networks Unfolds Informative Chronnectomics: A Novel Data-Driven Thresholding Scheme Based on Orthogonal Minimal Spanning Trees (OMSTs).

The human brain is a large-scale system of functionally connected brain regions. This system can be modeled as a network, or graph, by dividing the brain into a set of regions, or “nodes,” and quantifying the strength of the connections between nodes, or “edges,” as the temporal correlation in their patterns of activity. Network analysis, a part of graph theory, provides a set of summary statistics that can be used to describe complex brain networks in a meaningful way. The large-scale organization of the brain has features of complex networks that can be quantified using network measures from graph theory. The adaptation of both bivariate (mutual information) and multivariate (Granger causality) connectivity estimators to quantify the synchronization between multichannel recordings yields a fully connected, weighted, (a)symmetric functional connectivity graph (FCG), representing the associations among all brain areas. The aforementioned procedure leads to an extremely dense network of tens up to a few hundreds of weights. Therefore, this FCG must be filtered out so that the “true” connectivity pattern can emerge. Here, we compared a large number of well-known topological thresholding techniques with the novel proposed data-driven scheme based on orthogonal minimal spanning trees (OMSTs). OMSTs filter brain connectivity networks based on the optimization between the global efficiency of the network and the cost preserving its wiring. We demonstrated the proposed method in a large EEG database (N = 101 subjects) with eyes-open (EO) and eyes-closed (EC) tasks by adopting a time-varying approach with the main goal to extract features that can totally distinguish each subject from the rest of the set. Additionally, the reliability of the proposed scheme was estimated in a second case study of fMRI resting-state activity with multiple scans. Our results demonstrated clearly that the proposed thresholding scheme outperformed a large list of thresholding schemes based on the recognition accuracy of each subject compared to the rest of the cohort (EEG). Additionally, the reliability of the network metrics based on the fMRI static networks was improved based on the proposed topological filtering scheme. Overall, the proposed algorithm could be used across neuroimaging and multimodal studies as a common computationally efficient standardized tool for a great number of neuroscientists and physicists working on numerous of projects.

A Study on Facilities Location Using the Properties of Cut Set Matrix

This paper deals with a problem of facilities location. Fundamental suggestion is making an individual algorithm for combination of Presupposition and Objective in each problem. The presupposition of this paper is facilities locate straight, and the objective function is minimize Backward Distance Intensity. This new facilities algorithm to select minimum Backward Distance × Intensity location is developed by using a property on Cut Set matrix that is a part of graph theory. The feature of this algorithm is ability to select the optimal solution by only using easy matrices manipulation. Trial of this algorithm in regard to an actual 6 facilities is described here in.