The differential of the strong product graphs

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 tig...

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Bibliographic Details
Published in:International journal of computer mathematics 2015-06, Vol.92 (6), p.1124-1134
Main Authors: Bermudo, S., De la Torre, L., Martín-Caraballo, A.M., Sigarreta, J.M.
Format: Article
Language:English
Subjects:
differential
domination
Graph theory
Graphs
Mathematical analysis
Mathematical models
Parameter estimation
strong product graphs
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Summary: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.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2014.941359