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 $S^0(G)=\sum _{\{u,v\}\subset V(G)}(d_G(u)–d_G(v))d_G(u,v)$, 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.