Open AccessA Scientific Research Analysis to Identify Number of Components in a Graph
Author(s) -
Prajwala. N.B,
Indumathi. S.M
Publication year - 2019
Publication title -
international journal of recent technology and engineering
Language(s) - English
Resource type - Journals
ISSN - 2277-3878
DOI - 10.35940/ijrte.b1031.078219
Subject(s) - combinatorics , adjacency matrix , mathematics , adjacency list , vertex (graph theory) , diagonal , discrete mathematics , graph energy , wheel graph , graph , graph power , line graph , geometry
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.