Extremal Tricyclic Graphs With Respect To Schultz Index

Abstract

For a graph \(G = (V,E)\), the Schultz index of \(G\) is defined as \(S(G) = \sum\limits_{\{u,v \}\subseteq V(G)} (d_G(u) + d_G(v))d_G(u,v)\), where \(d_G(u)\) is the degree of the vertex \(u\) in \(G\), and \(d_G(u,v)\) is the distance between \(u\) and \(v\) in \(G\). In this paper, we investigate the Schultz index of tricyclic graphs. The \(n\)-tricyclic graphs with the minimum Schultz index are determined.