%0 Journal Article
%T A note on the first Zagreb index and coindex of graphs
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Milovanović, Igor
%A Matejić, Marjan
%A Milovanović, Emina
%A Khoeilar, Rana
%D 2021
%\ 06/01/2021
%V 6
%N 1
%P 41-51
%! A note on the first Zagreb index and coindex of graphs
%K Topological indices
%K first Zagreb index
%K first Zagreb coindex
%R 10.22049/cco.2020.26809.1144
%X Let $G=(V,E)$, $V=\{v_1,v_2,\ldots,v_n\}$, be a simple graph with $n$ vertices, $m$ edges and a sequence of vertex degrees $\Delta=d_1\ge d_2\ge \cdots \ge d_n=\delta$, $d_i=d(v_i)$. If vertices $v_i$ and $v_j$ are adjacent in $G$, it is denoted as $i\sim j$, otherwise, we write $i\nsim j$. The first Zagreb index is vertex-degree-based graph invariant defined as $M_1(G)=\sum_{i=1}^nd_i^2$, whereas the first Zagreb coindex is defined as $\overline{M}_1(G)=\sum_{i\nsim j} d_i+d_j)$. A couple of new upper and lower bounds for $M_1(G)$, as well as a new upper bound for $\overline{M}_1(G)$, are obtained.
%U http://comb-opt.azaruniv.ac.ir/article_14047_6dacca4d77087d8b3967a894b7a7d103.pdf