Extremal tetracyclic graphs with respect to the first and second Zagreb indices

Abstract

‎The first Zagreb index‎, ‎$M_1(G)$‎, ‎and second Zagreb index‎, ‎$M_2(G)$‎, ‎of the graph $G$ is defined as $M_{1}(G)=sum_{vin‎ ‎V(G)}d^{2}(v)$ and $M_{2}(G)=sum_{e=uvin E(G)}d(u)d(v),$ where‎ ‎$d(u)$ denotes the degree of vertex $u$‎. ‎In this paper‎, ‎the first‎ ‎and second maximum values of the first and second Zagreb indices‎ ‎in the class of all $n-$vertex tetracyclic graphs are presented‎.