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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     language = {en},
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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/