Strong global distribution center of graphs

Articles in Press

Document Type : Original paper

Authors

Department of Basic Sciences, Shahid Rajaee Teacher Training University, P.O. Box 16785-163, Tehran, Iran

Abstract

Let G=(V,E) be a graph. A strong global distribution center of G is a dominating set  S⊆V  such that for any v∈V∖S, there exists a vertex u∈N[v]∩S with the property |N[u]∩S|>|N[v]∩(V∖S)|. The strong global distribution center number, gdcs(G), of a graph G is the minimum cardinality of a strong global distribution center of G. In this paper, we introduce the concept of strong global distribution center. We give some bounds on the gdcs(G) for general graphs and classify graphs with extremal values of gdcs(G). Also, we compute the strong global distribution center number for some families of graphs and  study this parameter for some families of graph products.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 14 January 2025

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