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Graphs with Equal Domination, Connected Domination, and Watching Numbers | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 19 تیر 1405 اصل مقاله (418.47 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30851.2644 | ||
| نویسندگان | ||
| Kamran Mirasheh* 1؛ Ahmad Abbasi2؛ Ebrahim Vatandoost3 | ||
| 1Faculty of Mathematical Sciences University of Guilan, P. O. Box 41335-19141, Rasht, Iran | ||
| 2Faculty of Mathematical Sciences, University of Guilan, P. O. Box 41335-19141, Rasht, Iran | ||
| 3Department of Basic Science Imam Khomeini International University, P. O. Box 34148-96818, Qazvin, Iran | ||
| چکیده | ||
| This paper investigates how the parameters $\gamma(G)$, $\beta_c(G)$, and $\omega(G)$ influence and characterize the structure of a graph. We prove that if $G$ is of the form $H \odot K_1$, then $\gamma(G) = \beta_c(G) = \omega(G)$. Furthermore, under the assumption that $\gamma(G) = \beta_c(G) = \omega(G)$ and by leveraging properties of connected vertex covers and dominating sets, we show that $G$ belongs to a specific class of graphs. | ||
| کلیدواژه‌ها | ||
| Watching system؛ Dominating set؛ Connected vertex cover | ||
| مراجع | ||
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