Derangement Representation of Graphs

	Derangement Representation of Graphs
Communications in Combinatorics and Optimization
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 13 خرداد 1404
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2025.29684.2111
نویسندگان
Somayeh Ashofteh؛ Moharram N. Iradmusa^*
Department of Mathematical Sciences, Shahid Beheshti University, G.C., P.O. Box 19839-63113, Tehran, Iran
چکیده
A derangement $k$-representation of a graph $G$ is a map $\pi$ of $V(G)$ to the symmetric group $S_k$, such that for any two vertices $v$ and $u$ of $V(G)$, $v $ and $u$ are adjacent if and only if $\pi(v)(i) \neq \pi(u)(i)$ for each $i \in \{1,2,3,\ldots,k\}$. The derangement representation number of $G$ denoted by $drn(G)$, is the minimum of $k$ such that $G$ has a derangement $k$-representation. In this paper, we prove that any graph has a derangement $k$-representation. Also, we obtain some lower and upper bounds for $drn(G)$, in terms of the basic parameters of $G$. Finally, we determine the exact value or give the better bounds of the derangement representation number of some classes of graphs.
کلیدواژه‌ها
Derangement؛ Symmetric Group؛ Derangement Representation Number

آمار تعداد مشاهده مقاله: 8

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