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Total Roman domination on Kneser graphs | ||
| Transactions on Combinatorics | ||
| دوره 15، شماره 2، شهریور 2026، صفحه 69-76 اصل مقاله (2.37 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2025.140647.2148 | ||
| نویسندگان | ||
| Abolfazl Bahmani* ؛ Mojgan Emami | ||
| Department of Mathematics, University of Zanjan, Zanjan, Iran | ||
| چکیده | ||
| A Roman dominating function (RDF) on a graph $G$ is a function $f : V (G) \longrightarrow \{0, 1, 2\}$ such that any vertex $v$ with $ f(v) = 0$ is adjacent to at least one vertex $w$ with $f(w) = 2$. In addition, if the subgraph of $G$ induced by the set of all vertices for which $f \ne 0$ has no isolated vertices then $f$ is called a total Roman dominating function (TRDF). If $f$ is an RDF (TRDF) then the least value of $\sum_{u\in V} f(u)$ is called Roman domination number (total Roman domination number) of $G$ and is denoted by $\gamma_{_R}(G)$ ( $\gamma_{_{tR}}(G)$). Let $G=G(n, k, 0)$ be a Kneser graph, where $n,k$ are positive integers. In this paper we present some bounds for $\gamma_{_{tR}}(G(n, k, 0))$ for $k^2 < n < k^2+k$. In particular we show that $\gamma_{_{tR}}(G(k^2+k-1, k, 0))=2(k+2)$ and for $n\geqslant 2k+1$, $\gamma_{_{R}}(G(n, k, 0)) \geq max \{ \gamma_{_{R}}(G(n-1, k -1, 0)), \gamma_{_{R}}(G(n, k -1, 0))\}$. | ||
| کلیدواژهها | ||
| Total Roman domination number؛ Kneser graph | ||
| مراجع | ||
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[1] H. A. Ahangar, M. A. Henning, V. Samodivkin and I. G. Yero, Total Roman domination in graphs, Appl. Anal. Discrete Math., 10 no. 2 (2016) 501–517. [11] D. B. West, Introduction to graph theory, Prentice Hall, Inc., Upper Saddle River, NJ, 1996. | ||
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آمار تعداد مشاهده مقاله: 379 تعداد دریافت فایل اصل مقاله: 322 |
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