Geodesic
On hyper-Zagreb index and coindex
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 42 (2017) no. 1.

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Let $G$ be a graph with vertex set $\mathbf V$ and edges set $\mathbf E$. By $d(v)$ is denoted the degree of its vertex $v$. Two much studied degree--based graph invariants are the first and second Zagreb indices, defined as $M_1=\sum\limits_{u \in \mathbf V} d(u)^2$ and $M_2 = \sum\limits_{uv \in \mathbf E} d(u)\,d(v)$. A~recently proposed new invariant of this kind is the hyper--Zagreb index, defined as $HZ = \sum\limits_{uv \in \mathbf E} [d(u)+d(v)]^2$. The basic relations between this index and its coindex for a graph $G$ and its complement $\overline G$ are determined. 
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Ivan Gutman. On hyper-Zagreb index and coindex. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 42 (2017) no. 1. http://geodesic.mathdoc.fr/item/BASS_2017_42_1_a0/