A Scientific Research Analysis to Identify Number of Components in a Graph
1Prajwala.N.B: Department of Computer Science, Amrita School of Arts & Sciences, Mysuru, Amrita Vishwa Vidyapeetham, India.
2Indumathi.S.M: Department of Computer Science, Amrita School of Arts & Sciences, Mysuru, Amrita Vishwa Vidyapeetham, India.
Manuscript received on 08 March 2019 | Revised Manuscript received on 15 March 2019 | Manuscript published on 30 July 2019 | PP: 774-778 | Volume-8 Issue-2, July 2019 | Retrieval Number: B1031078219/19©BEIESP | DOI: 10.35940/ijrte.B1031.078219
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: In this work a method to find number of components, possible connection and not possible connection between nodes in a graph are proposed. Graphs are represented as adjacency matrix. The elements of adjacency matrix can be any integer, 0 represents that there is no edge between vertices, any integer greater than 0 indicates that there are 1 or more edges between nodes, 2 in diagonal if the vertices have self-loops. The sum of any rows or columns gives the degree of the vertex. If the sum is zero that indicates that the vertex is isolated vertex, isolated vertex also forms a component. The point of disconnectivity in the graph is identified from the adjacency matrix, the total number of components will be summation of isolated vertices, number of disconnectivity pattern +1. Some observations on adjacency matrix are made to find point of disconnectivity and number of components in a graph.
Keywords: Adjacency Matrix, Components, Connectivity, Disconnectivity, Point of Disconnectivity.
Scope of the Article: Industrial, Financial and Scientific Applications of All Kind