On the extremal cactus graphs for variable sum exdeg index with a fixed number of cycles. Issue 3 (1st September 2020) - Javaid, Mubeen; Ali, Akbar; Milovanović, Igor; Milovanović, Emina
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 SEI a ( G ) = ∑ v ∈ V ( G ) d v a d v, 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 k ≥ 0, let C n, k be the class of all n -vertex cacti with k cycles. The present paper is devoted to find the graphs with minimal and maximal SEI a values among all the members of the graph class C n, k for a  > 1.