Maximal Graphs of the First Reverse Zagreb Beta Index

Abstract

The reverse vertex degree of a vertex v of a simple connected graph G defined as; c(v) = Delta - d(v) + 1 where Delta denotes the largest of all degrees of vertices of G and d(v) denotes the number of edges incident to v. The first reverse Zagreb beta index of a simple connected graph G defined as; CM1 beta (G) = Sigma(uv is an element of E(G)) (c(u) + c(v)). In this paper we characterized maximal graphs with respect to the first reverse Zagreb beta index.