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

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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 
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/
@article{KJM_2020_44_4_a1,
     author = {N. Dehgardi and H. Aram},
     title = {Sharp {Bounds} on the {Augmented} {Zagreb} {Index} of {Graph} {Operations}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {509 },
     year = {2020},
     volume = {44},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2020_44_4_a1/}
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