Extremal Zagreb Indices of Unicyclic Graphs

Abstract

The Zagreb indices are topological indices of graphs, which are defined as:\(M_1(G) = \sum\limits_{v \in V(G)} (d(v))^2\), \(M_2(G) = \sum\limits_{uv \in E(G)} d(u)d(v)\) .In this paper, we determine the upper and lower bounds for the Zagreb indices of unicyclic graphs in terms of their order and girth. In each case, we characterize the extremal graphs.