Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 11 3 2026 09 01 Strong global distribution center of graphs 1047 1057 14881 10.22049/cco.2025.29903.2217 EN Mostafa Edalat Department of Basic Sciences, Shahid Rajaee Teacher Training University, P.O. Box 16785-163, Tehran, Iran Hamidreza Maimani Department of Basic Sciences, Shahid Rajaee Teacher Training University, P.O. Box 16785-163, Tehran, Iran Journal Article 2024 07 20 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. https://comb-opt.azaruniv.ac.ir/article_14881_2f3c20535e87868ce1f5c1a0cef23d51.pdf