@article {
author = {Milovanović, Igor and Matejić, Marjan and Milovanović, Emina and Khoeilar, Rana},
title = {A note on the first Zagreb index and coindex of graphs},
journal = {Communications in Combinatorics and Optimization},
volume = {6},
number = {1},
pages = {41-51},
year = {2021},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2020.26809.1144},
abstract = {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. },
keywords = {Topological indices,first Zagreb index,first Zagreb coindex},
url = {http://comb-opt.azaruniv.ac.ir/article_14047.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_14047_6dacca4d77087d8b3967a894b7a7d103.pdf}
}