Strict Lower Bounds On The Multiplicative Zagreb Indices Of Graph Operations

Nezhad, F.Falahati; Iranmanesh, A.; Tehranian, A.; Azari, M.

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Ars Combinatoria

Volume 117
Pages: 399-409

Research article

Strict Lower Bounds On The Multiplicative Zagreb Indices Of Graph Operations

^¹, ^², ^¹, ^³

¹Department of Mathematics, Science and Research Branch, Islamic Azad University, P.O. Box: 14515-1775, Tehran, Iran

²Department of Mathematics, Tarbiat Modares University, P.O. Box: 141 15-137, Tehran, Iran

³Department of Mathematics, Kazerun Branch, Islamic Azad University, P. O. Box: 73135-168, Kazerun, Iran

Published: 31/10/2014

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Abstract

The first and second multiplicative Zagreb indices of a simple graph $G$ are defined as:
$\prod_{1} (G) = \prod_{u \in V (G)} d_{G} (u)^{2} and \prod_{2} (G) = \prod_{u v \in E (G)} d_{G} (u) d_{G} (v),$
where $d_{G} (u)$ denotes the degree of the vertex $u$ of $G$ . In this paper, we establish strict lower bounds on the first and second multiplicative Zagreb indices of various graph operations in terms of the first and second multiplicative Zagreb indices and multiplicative sum Zagreb index of their components.

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Ars Combinatoria

Strict Lower Bounds On The Multiplicative Zagreb Indices Of Graph Operations

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