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Strong global distribution center of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 20، دوره 11، شماره 3، آذر 2026، صفحه 1047-1057 اصل مقاله (381.04 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.29903.2217 | ||
| نویسندگان | ||
| Mostafa Edalat؛ Hamidreza Maimani* | ||
| Department of Basic Sciences, Shahid Rajaee Teacher Training University, P.O. Box 16785-163, Tehran, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Global distribution center؛ Strong global distribution center؛ Dominating set؛ Graphs products | ||
| مراجع | ||
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[7] I.G. Yero, M. Jakovac, and D. Kuziak, On global (strong) defensive alliances in some product graphs, Commu. Comb. Optim. 2 (2017), no. 1, 21–33. https://doi.org/10.22049/cco.2017.13595 | ||
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