Majid Aghel - Ferdowsi University of Mashhad, International Campus
Ahmad Erfanian - Ferdowsi University
Ali Reza Ashrafi - University of Kashan

‎Let $G$ be a simple graph‎. ‎The graph $G$ is called a quasi unicyclic graph if there exists a vertex $x \in V(G)$ such that $G-x$ is a connected graph with a unique cycle‎. ‎Moreover‎, ‎the first and the second Zagreb indices of $G$ denoted by $M_۱(G)$ and $M_۲(G)$‎, ‎are the sum of $\deg^۲(u)$ overall vertices $u$ in $G$ and the sum of $\deg(u)\deg(v)$ of all edges $uv$ of $G$‎, ‎respectively‎. ‎The first and the second Zagreb indices are defined relative to the degree of vertices‎. ‎In this paper‎, ‎sharp upper and lower bounds for the first and the second Zagreb indices of quasi unicyclic graphs are given‎.

‎First Zagreb index‎, Second Zagreb index‎, Quasi Unicyclic graphs