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 [Formula: see text] , where [Formula: see text] is the degree of vertex [Formula: see text] , a is a positive real number different from 1. In this paper, we defined sub-collections of tricyclic graphs say [Formula: see text] and [Formula: see text]. 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 [Formula: see text]-value from [Formula: see text].