Affiliation:
1. College of General Education, Guangdong University of Science and Technology, Dongguan 523083, China
2. School of Mathematics and Statistics, Central South University, Changsha 410083, China
Abstract
For a connected graph G with vertex set V, denote by d(v) the degree of vertex v and d(u, v) the distance between u and v. The value Gut(G)=∑{u,v}⊆Vd(u)d(v)d(u,v) is called the Gutman index of G. Recently, the graph minimizing the Gutman index among unicyclic graphs with pendent edges was characterized. Denoted by U(n,m) the set of unicyclic graphs on n vertices with matching number m. Motivated by that work, in this paper, we obtain a sharp lower bound for Gutman index of graphs in U(n,m), and the extremal graph attaining the bound is also obtained. It is worth noticing that all the extremal graphs are of high symmetry, that is, they have large automorphic groups.
Funder
National Natural Science Foundation of China
Foundation of Guangdong University of Science and Technology
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
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