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Upper Bounds for the Modified Second Multiplicative Zagreb Index of Graph Operations

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Abstract:

The modified second multiplicative Zagreb index of a connected graph G, denoted by $\prod_{2}^{*}(G)$, is defined as $\prod_{2}^{*}(G)=\prod \limits_{uv\in E(G)}[d_{G}(u)+d_{G}(v)]^{[d_{G}(u)+d_{G}(v)]}$ where $d_{G}(z)$ is the degree of a vertex z in G. In this paper, we present some upper bounds for the modified second multiplicative Zagreb index of graph operations such as union, join, Cartesian product, composition and corona product of graphs are derived.The modified second multiplicative Zagreb index of aconnected graph , denoted by , is defined as where is the degree of avertex in . In this paper, we present some upper bounds for themodified second multiplicative Zagreb index of graph operations such as union,join, Cartesian product, composition and corona product of graphs are derived.

Info:

Periodical:
Bulletin of Mathematical Sciences and Applications (Volume 17)
Pages:
10-16
DOI:
10.18052/www.scipress.com/BMSA.17.10
Citation:
B. Basavanagoud and S. Patil, "Upper Bounds for the Modified Second Multiplicative Zagreb Index of Graph Operations", Bulletin of Mathematical Sciences and Applications, Vol. 17, pp. 10-16, 2016
Online since:
Nov 2016
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