Geodesic
New Upper and Lower Bounds for Some Degree-based Graph Invariants
Kragujevac Journal of Mathematics, Tome 44 (2020) no. 2, p. 181 .

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

For a simple graph $G$ with vertex set $V(G)$ and edge set $E(G)$, let $\deg(u)$ be the degree of the vertex $u \in V(G)$. The forgotten index of $G$ and its coindex are defined as $F(G)=\sum_{v\in V(G)}\deg^3(v)$ and $\overline{F}(G) = \sum_{uv\not\in E(G)}\big[\deg^2(u)+\deg^2(v)\big]$. New bonds for the first Zagreb index $M_1(G)=\sum_{v \in V(G)}\deg(v)^2$, forgotten index, and its coindex are obtained.
Classification : 05C07, 05C90
Keywords: degree (of vertex), coindex, forgotten index, $F$-index, Zagreb index 
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     author = {A. Ghalav and A. Ashrafi and I. Gutman},
     title = {New {Upper} and {Lower} {Bounds} for {Some} {Degree-based} {Graph} {Invariants}},
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A. Ghalav; A. Ashrafi; I. Gutman. New Upper and Lower Bounds for Some Degree-based Graph Invariants. Kragujevac Journal of Mathematics, Tome 44 (2020) no. 2, p. 181 . http://geodesic.mathdoc.fr/item/KJM_2020_44_2_a1/