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  $S\subseteq V$  such that for any $v\in V\setminus S$, there exists a vertex $u\in N[v]\cap S$ with the property $|N[u]\cap S|> |N[v]\cap (V\setminus S)|$. The strong global distribution center number, gdc$^s(G)$, 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 gdc$^s(G)$ for general graphs and classify graphs with extremal values of gdc$^s(G)$. 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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