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 $M_1(G)$ and $M_2(G)$, are the sum of $\deg^2(u)$ 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.
Aghel, M., Erfanian, A., & Ashrafi, A. R. (2019). On the first and second Zagreb indices of quasi unicyclic graphs. Transactions on Combinatorics, 8(3), 31-40. doi: 10.22108/toc.2019.115147.1615
MLA
Majid Aghel; Ahmad Erfanian; Ali Reza Ashrafi. "On the first and second Zagreb indices of quasi unicyclic graphs". Transactions on Combinatorics, 8, 3, 2019, 31-40. doi: 10.22108/toc.2019.115147.1615
HARVARD
Aghel, M., Erfanian, A., Ashrafi, A. R. (2019). 'On the first and second Zagreb indices of quasi unicyclic graphs', Transactions on Combinatorics, 8(3), pp. 31-40. doi: 10.22108/toc.2019.115147.1615
VANCOUVER
Aghel, M., Erfanian, A., Ashrafi, A. R. On the first and second Zagreb indices of quasi unicyclic graphs. Transactions on Combinatorics, 2019; 8(3): 31-40. doi: 10.22108/toc.2019.115147.1615
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