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Exact double domination in subdivision, Mycielskian and middle graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 12 اردیبهشت 1404 اصل مقاله (424.59 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.29949.2235 | ||
| نویسندگان | ||
| Ali Behtoei* ؛ Rozhin Zarifian | ||
| Department of Mathematics, Faculty of Science, Imam Khomeini International University, PO Box: 34148 - 96818, Qazvin, Iran | ||
| چکیده | ||
| An exact doubly dominating set (also called an efficient doubly dominating set in [F. Harary and T.W. Haynes, Double domination in graphs, Ars Combin. 55 (2000), 201–213]) for a graph $G=(V,E)$ is a subset $D$ of vertices such that each vertex of $G$ is dominated by exactly two vertices of $D$. In this paper we show that subdivision graphs admit exact doubly dominating sets under specific conditions, while Mycielskian and middle graphs do not. We provide some characterizations and we investigate the existence of exact doubly dominating sets for their complements. | ||
| کلیدواژهها | ||
| Exact double domination؛ subdivision؛ middle؛ Mycielskian | ||
| مراجع | ||
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[16] R.Y. Salkhori, E. Vatandoost, and A. Behtoei, 2-rainbow domination number of the subdivision of graphs, Commun. Comb. Optim. to appear (2025), https://doi.org/10.22049/cco.2024.28850.1749 | ||
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