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; cv = ? ? dv + 1 where ? denotes the largest of all degrees of vertices of G and dv denotes the number of edges incident to v. The first reverse Zagreb beta index of a simple connected graph G defined as; CM?1 (G) = P uv?E(G)(cu + cv). In this paper we characterized maximal graphs with respect to the first reverse Zagreb beta index.