Conjugated tricyclic graphs with maximum variable sum exdeg index

Abstract

The variable sum exdeg index, initially introduced by Vukicevic (2011) [20] for predicting the octanol water partition co-efficient of certain chemical compounds, is an invariant for a graph G and defined as SEIa(G)=∑v∈V(G)(dvadv), where dv is the degree of vertex v∈V(G), a is a positive real number different from 1. In this paper, we defined sub-collections of tricyclic graphs say T2m3,T2m4,T2m6 and T2m7. The graph with maximum variable sum exdeg index is characterized from each collection given above with perfect matching. Consequently, through a comparison among these extremal graphs, we indicate the graph which contains maximum SEIa-value from T2m.