MMN-1274
Sharp bounds for the first Zagreb index andfirst Zagreb coindex
Abstract
Let $G$ be an undirected connected graph with $n\,,\,n \geq 2$, vertices
and $m$ edges with vertex degrees $\Delta =d_1\ge d_2 \ge \cdots \ge d_n=\delta$. Lower and upper bounds of a graph invariants $M_1=\sum_{i=1}^nd_i^2$, referred to as the first Zagreb index, and $\bar M_1 =\sum_{i\nsim j}(d_i+d_j)$, named the first Zagreb coindex, depending on parameters $n$, $m$, $\Delta$ and $\delta$ are obtained. The obtained results represent improvement of the results reported in the literature.
Vol. 16 (2015), No. 2, pp. 1017-1024