Geodesic
New Upper and Lower Bounds for Some Degree-based Graph Invariants
Kragujevac Journal of Mathematics, Tome 44 (2020) no. 2, p. 181 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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 
@article{KJM_2020_44_2_a1,
     author = {A. Ghalav and A. Ashrafi and I. Gutman},
     title = {New {Upper} and {Lower} {Bounds} for {Some} {Degree-based} {Graph} {Invariants}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {181 },
     year = {2020},
     volume = {44},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2020_44_2_a1/}
}
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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/