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International Journal of Computer Mathematics Volume 92, 2015 - Issue 6
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Section A

The differential of the strong product graphs

S. BermudoDepartment of Economics, Quantitative Methods and Economic History, Pablo de Olavide University, Carretera de Utrera Km. 1, 41013-Sevilla, SpainCorrespondence[email protected]
,
L. De la TorreDepartment of Mathematical Analysis, University of Sevilla, Aptdo. 1160, 41080-Sevilla, Spain
,
A.M. Martín-CaraballoDepartment of Economics, Quantitative Methods and Economic History, Pablo de Olavide University, Carretera de Utrera Km. 1, 41013-Sevilla, Spain
&
J.M. SigarretaFaculty of Mathematics, Autonomous University of Guerrero, Carlos E. Adame 5, Col. La Garita, Acapulco, Guerrero, Mexico
Pages 1124-1134 | Received 03 Apr 2013, Accepted 30 Jun 2014, Published online: 28 Jul 2014
 
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Abstract

Let G=(V, E) be a graph of order n and let B(D) be the set of vertices in V ∖ D that have a neighbour in the set D. The differential of a set D is defined as ∂ (D)=|B(D)|−|D| and the differential of a graph to equal the maximum value of ∂(D) for any subset D of V. In this paper we obtain several tight bounds for the differential of strong product graphs. In particular, we investigate the relationship between the differential of this type of product graphs and various parameters in the factors of the product.

2010 AMS Subject Classifications:

Acknowledgements

This work was partly supported by Plan Nacional Grant MTM2012-35107, Junta de Andalucía FQM-260 and CONACYT-UAG I0110/62/10 (México).

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