Unicyclic and bicyclic graphs with maximum exponential second Zagreb index

Abstract

The exponential second Zagreb index of a connected graph G, denoted by eM(G), is defined as the sum of the weights ed over all edges uv∈E(G), where dG(u) denotes the degree of vertex u. The maximum value of eM in the class of connected acyclic graphs has already been studied. In this paper, maximal unicyclic and bicyclic graphs of order n with respect to eM are represented. © 2021 Elsevier B.V.