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INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 9, ISSUE 04, APRIL 2020 ISSN 2277-8616

A Study On Use Of Graph In Engineering Through Graphtea Software

Dr.M.Thamizhsudar ,Dr.A.K.Bhuvaneswari

Abstract: The aim of the paper is to letting know the readers about the availability of the software Graph tea which is very helpful to run the of Graph theory. Here some of the Graph theory problems were taken from the of Computer science engineering and are illustrated using Graph tea and the corresponding outputs are shown here.

Index Terms: Algorithms, Examples, GraphTea, Graph theory, output, Software, Spanning ——————————  ——————————

1 INTRODUCTION 2.1 Shortest Graph theory is the study of graphs where the graphs are The is about finding a path created by connecting the vertices through the edges. For between two vertices in a graph such that the total sum of the example, Routes (edges) between the cities (vertices) can be edges weights is minimum. Particularly if all edge weights represented using graphs. Graph theory has several were one, Bellman Ford’s Algorithm (BFS) could be used , for applications in the field of engineering and science. In the other values of weights, either of Dijkstra’s Algorithm and Science, the molecular structure and chemical structure of a Floyd-Warshall’s algorithm could be used . substance, the DNA structure of an organism, etc., are represented by graphs .In electrical engineering, the concepts 2.2 Mnimum Algorithm: of graph theory is used extensively in designing circuit This algorithm is used in designing networks. It is also used for connections. For detailed study on applications of graph theory approximating the travelling salesman problem, multi-terminal on various fields one can refer [1]. Graph theory has many minimum problem and minimum-cost weighted perfect applications in the field of Computer science engineering. It is . Other practical applications are:Cluster used in design, network and , circuit Analysis,Handwriting recognition and Image segmentation. designing etc., The graphs for transportation systems, Famous algorithms for finding the are where intersection of two (or more) roads are considered to be Kruskal’s algorithms and Prim’s algorithm, both can be easily a and the road connecting two vertices is considered to run on GraphTea. Some examples are given here, be an edge, thus their navigation system is based on the algorithm to calculate the shortest path between two vertices. Example-1-Kruskal Algorithm Apart from this, Graph theory concepts are used in Google maps [2]. Algorithms play a major role in computer science engineering. Relationships among interconnected computers in the network follow the principles of graph theory. Using these algorithms, many theoretical problems can be solved [3]. Graphtea is the open source software exclusively for graph theory. Using this software we can generate graphs, We can obtain shortest paths, minimum spanning tree etc., and in particular, Graphtea can be used as a tool effectively and easily for running algorithms. Fig1 Actual graph for Kruskal algorithm 2 ALGORITHMS Most of the network problems were modelled as graph and The graph in Fig1 was generated in Graphtea Software to find various algorithms were available to solve these problems. the minimum spanning tree. We got the output as in Fig2 in Some of the algorithms were listed below. The same were which the minimum spanning tree was highlighted with pink available in GraphTea. colour.

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• Dr.M.Thamizhsudar, Assistant Professor, Department of , Aarupadaiveedu Institute of technology(Vinayaka Missions Research Foundation deemed to be university ,salem),Vinayaka nagar,OMR, KancheepuramDT-603 104. Tamil Nadu, INDIA, PH-918754541025. E-mail: [email protected] • Dr.A.K.Bhuvaneswari, , Assistant Professor,Department of Mathematics, Aarupadaiveedu Institute of technology(Vinayaka Fig2 Output for Kruskal algorithm through Graphtea Missions Research Foundation deemed to be university, salem),Vinayaka nagar,OMR, KancheepuramDT-603 104. Minimum Spanning tree from the output is TamilNadu,INDIA, PH-918754541025. E-mail: [email protected] {a-c, a-b, c-d, c-e, b-e, d-f }. 2958 IJSTR©2020 www.ijstr.org INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 9, ISSUE 04, APRIL 2020 ISSN 2277-8616

scholar may also avail the features available in Graphtea for Same way we can get output for Prim’s algorithm their research work.

Example-2 Prim’s Algorithm 4 REFERENCES [1]. Bhagya Jyoti Nath, :‖ Applications of Graph Theory in different Branches of Science‖, International Journal of Mathematics and its applications, Vol-5,Issue 3-A,57- 60,2017 [2]. https://www.geekforgeeks.org/applications-of-graph- / [3]. S.G. Shrinivas et. al.‖ Applications of Graph Theory in computer science –an overview ―, International Journal of Engineering Science and Technology, Vol. Fig3 Actual Graph for Prim’s algorithm 2(9), 2010, 4610-4621, 2010. [4]. M. Ali Rostami, Azin Azadi, and Masoumeh The graph in Fig3 was given in Graphtea Software to find the Seydi.‖GraphTea: Interactive Graph Self-Teaching minimum spanning tree using Prim’s algorithm. We got the Tool‖, Communications, Circuits and Educational output as in fig4 Technologies, ISBN: 978-1-61804-231-6, 48-51. [5]. Bala Bhaskara Rao Emani , Satya Srinivas Maddipati, Reddy Krishna Rao.,‖ Graph Tea: Simulating Tool for Graph Theory & Algorithms‖, International Journal for Modern Trends in Science and Technology,Vol(2), Issue:06,88-91,2016 [6]. https://math.stackexchange.com [7]. https://www.hackerearth.com/practice/algorithms/ graphs/shortest-path-algorithms/tutorial/ [8]. https:// en. Wikipedia.org/wiki/depth-first search

Fig4 Output for Prim’s algorithm through Graphtea.

The Minimum Spanning Tree for the given graph is shown in the report that {A-B, B-C, C-D, A-E, A-F, D-G, D-H}.

2.3 Maximum Flow and Minimum Cut In graph theory, a is defined as a involving a source(S) and a sink (T) and several other nodes connected with edges. The algorithm available for finding Maximum flow and Minimum cut in a given network.

2.4Depth First search Depth-first search (DFS) (available in Graphtea) is an used to search a graph or tree data structure. For detailed study can refer web reference [7].This algorithm is used to find the bridges of graphs, biconnectivity of graphs, to find connected components etc. Apart from these, algorithms to find the , cycles in graph, acyclic checker, just a sample, Network generator, Topological sort, cholesky algorithms were available in GraphTea. For more detailed study on GraphTea one can refer [4] and [5].

3 CONCLUSION As Graph theory has applications in almost every branch of engineering, Any engineering student can make use of the software Graph Tea for their project work, and the research 2959 IJSTR©2020 www.ijstr.org