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Multiset Dimension of Prisms | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 05 فروردین 1404 اصل مقاله (2.14 M) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.29101.1852 | ||
| نویسندگان | ||
| Reginaldo M. Marcelo؛ Agnes D. Garciano؛ Jude Cabigas Buot* ؛ Mark Anthony C. Tolentino | ||
| Department of Mathematics, Ateneo de Manila University, Quezon City, Philippines | ||
| چکیده | ||
| Given a subset $W$ of the vertex set of a graph $G$, the representation multiset $r_m(v|W)$ of a vertex $v$ is the multiset of distances between $v$ and each vertex in $W$. The subset $W$ is called an m-resolving set of $G$ if distinct vertices have distinct representation multisets. Introduced independently by Saenpholphat and Simanjuntak et al., the m-resolving sets of a graph can be used to uniquely identify its vertices. The notion of m-resolving sets has been shown to be equivalent to identification colorings that have been introduced by Chartrand et al. More recently, Kono and Zhang have established that the prism $K_2 \Box C_n$ has an m-resolving set (equivalently, identification coloring) if and only if $n \geq 6$. In this work, we extend their result by determining the multiset dimension of prisms; that is, we determine the minimum cardinality of their m-resolving sets. | ||
| کلیدواژهها | ||
| m-resolving set؛ identification coloring؛ multiset dimension؛ prism | ||
| مراجع | ||
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