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REGULAR NUMBER OF SUBDIVISION OF MIDDLE GRAPH OF A GRAPH

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Kalshetti Swati Mallinath, Vishwas
» doi: 10.48047/ecb/2023.12.si4.1749

Abstract

The middle graph of a subdivision of a graph, represented by M[S(G)], for any (p,q) graph G, is a graph whose vertex set is V[S(G)]∪E[S(G)]; If two edges of G are next to one other or if one is a vertex and the other is an edge incident with it, those two points are said to be adjacent. The least number of sub-sets into which the edge set of the M[S(G)] should be divided in order to generate a regular subgraph for each subset is known as the regular number of the M[S(G)] and is indicated by the symbol r_sm (G). Several findings on the regular number of r_sm (G) were made and expressed in terms of G elements in this article.

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