On the extremal cactus graphs for variable sum exdeg index with a fixed number of cycles

Abstract

The variable sum exdeg index, introduced by Vukičević [Croat. Chem. Acta 84 (2011) 87–91] for predicting the octanol-water partition coefficient of certain chemical compounds, of a graph G is defined as where a is any positive real number different from 1, V(G) is the vertex set of G and dv denotes the degree of a vertex v. A connected graph G is a cactus if and only if every edge of G lies on at most one cycle. For n > 3 and let be the class of all n-vertex cacti with k cycles. The present paper is devoted to find the graphs with minimal and maximal values among all the members of the graph class for a > 1.

Keywords

• topological index
• variable sum exdeg index
• extremal problem
• cactus graph