TY - JOUR
ID - 14047
TI - A note on the first Zagreb index and coindex of graphs
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Milovanović, Igor
AU - Matejić, Marjan
AU - Milovanović, Emina
AU - Khoeilar, Rana
AD - Faculty of Electronic Engineering, Nis, Serbia
AD - Faculty of Electronic Engineering
AD - Azarbaijan Shahid Madani University
Y1 - 2021
PY - 2021
VL - 6
IS - 1
SP - 41
EP - 51
KW - Topological indices
KW - first Zagreb index
KW - first Zagreb coindex
DO - 10.22049/cco.2020.26809.1144
N2 - 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.
UR - http://comb-opt.azaruniv.ac.ir/article_14047.html
L1 - http://comb-opt.azaruniv.ac.ir/article_14047_6dacca4d77087d8b3967a894b7a7d103.pdf
ER -