Conjugated tricyclic graphs with maximum variable sum exdeg index

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 $$, where $$ is the degree of vertex $$, a is a positive real number different from 1. In this paper, we defined sub-collections of tricyclic graphs say $$ and $$. The graph with maximum variable sum exdeg index is characterized from each collection given above with perfect matching. Consequently, through a comparison among these extremal graphs, we indicate the graph which contains maximum $$-value from $$.