Padmakar-Ivan index of some types of perfect graphs

Abstract

The Padmakar-Ivan (PI) index of a graph G is defined as P I(G) = e∈E(G) (|V (G)| − NG(e)), where NG(e) is the number of equidistant vertices for the edge e. A graph is perfect if for every induced subgraph H, the equation χ (H) = ω (H) holds, where χ (H) is the chromatic number and ω (H) is the size of a maximum clique of H. In this paper, the PI index of some types of perfect graphs is obtained. These types include co-bipartite graphs, line graphs, and prismatic graphs.