The Co-PI Index of Some Compound Graphs

Abstract

Let \(G\) be a graph and \(u\) be a vertex of \(G\). The transmission index of \(u\) in \(G\), denoted by \(T_G(u)\), is the sum of distances from \(u\) to all the other vertices in graph \(G\), i.e., \(T(u) = T_G(u) = \sum_{v \in V} d_G(u,v)\). The Co-PI index [1] is defined as \(Co\text{-}PI(G) = \sum_{uv \in E(G)} |T(u) – T(v)|\). In this paper, we give some upper bounds for the Co-PI indices of the join, composition, disjunction, symmetric difference, and corona graph \(G_1 \circ G_2\).