Padmakar-Ivan Index of Some Types of Perfect Graphs

Abstract

The Padmakar-Ivan (PI) index of a graph G is defined as PI ( G ) = (cid:80) e ∈ E ( G ) ( | V ( G ) | − N G ( e )) , where N G ( 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.