Geodesic
Sharp Bounds on the Augmented Zagreb Index of Graph Operations
Kragujevac Journal of Mathematics, Tome 44 (2020) no. 4, p. 509

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 finite and simple graph with edge set $E(G)$. The { augmented Zagreb index} of $G$ is $AZI(G)=um_{uvı E(G)}eft(\frac{d_{G}(u)d_{G}(v)}{d_{G}(u)+d_{G}(v)-2}\right)^3,$ where $d_{G}(u)$ denotes the degree of a vertex $u$ in $G$. In this paper, we give some bounds of this index for join, corona, cartesian and composition product of graphs by general sum-connectivity index and general Randić index and compute the sharp amount of that for the regular graphs.
Classification : 05C12 05C07
Keywords: augmented Zagreb index, general sum-connectivity index, general Randić index, graph operations 
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     author = {N. Dehgardi and H. Aram},
     title = {Sharp {Bounds} on the {Augmented} {Zagreb} {Index} of {Graph} {Operations}},
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     year = {2020},
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N. Dehgardi; H. Aram. Sharp Bounds on the Augmented Zagreb Index of Graph Operations. Kragujevac Journal of Mathematics, Tome 44 (2020) no. 4, p. 509 . http://geodesic.mathdoc.fr/item/KJM_2020_44_4_a1/