Tricyclic Graphs With Minimum Modified Schultz Index And Maximum Zagreb Indices

Abstract

For a graph \(G = (V, E)\), the modified Schultz index of \(G\) is defined as \(S^0(G) = \sum\limits_{\{u,v\} \subset V(G)} (d_G(u) – d_G(v)) d_{G}(u, v)\), where \(d_G(u)\) (or \(d(u)\))is the degree of the vertex \(u\) in \(G\), and \(d_{G}(u, v)\) is the distance between \(u\) and \(v\). The first Zagreb index \(M_1\) is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index \(M_2\) is equal to the sum of the products of the degrees of pairs of adjacent vertices. In this paper, we present a unified approach to investigate the modified Schultz index and Zagreb indices of tricyclic graphs. The tricyclic graph with \(n\) vertices having minimum modified Schultz index and maximum Zagreb indices are determined.