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Roman Coalition Partitions in Graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 01 اردیبهشت 1405 اصل مقاله (423.34 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30582.2542 | ||
| نویسندگان | ||
| Juan Carlos Valenzuela Tripodoro* 1؛ Mustapha Chellali2؛ Hamidreza Golmohammadi3 | ||
| 1Department of Mathematics, University of C´adiz, Spain | ||
| 2LAMDA-RO Laboratory, Dept. of Mathematics, Univ. of Blida, Blida, Algeria | ||
| 3Sobolev Institute of Mathematics, Ak. Koptyug av. 4, Novosibirsk, 630090, Russia 2) Sobolev Institute of Mathematics, Ak. Koptyug av. 4, Novosibirsk, 630090, Russia | ||
| چکیده | ||
| The Roman domination problem is a combinatorial optimization problem on a graph asking to assign a label from $\{0,1,2\}$ to each vertex feasibly, such that the total sum of assigned labels is minimized. Let $G=(V,E)$ be a graph, and let \(U_1, U_2\subseteq V\) be two non-empty disjoint subsets. We say that the pair \( \{U_1,U_2\}\) is Roman-feasible if there exists a Roman dominating function \(f:V\to \{0,1,2\}\) such that \(V_0=V\setminus (U_1\cup U_2),\) \(V_1=U_i\) and \(V_2=U_{3-i}\) for some \(i\in \{1,2\},\) where $V_j$ denotes the set of vertices assigned label $j$ by $f$. The set \(\{U_1,U_2,U_3\}\) is a Roman coalition if the following two conditions hold: (i) the pair \(\{U_i,U_j\}\) is not Roman-feasible for any different \(1\le i,j\le 3;\) (ii) there exists \(k\) such that the pair \(\{U_i\cup U_j, U_k\}\) is Roman-feasible, where \(\{i,j,k\}=\{1,2,3\}.\) The purpose of this paper is to introduce and study the new concept of Roman coalitions in graphs, providing basic properties, lower and upper bounds, as well as exact values in specific cases. | ||
| کلیدواژه‌ها | ||
| Coalition؛ Roman coalition؛ Roman dominating set؛ Roman coalition partition | ||
| مراجع | ||
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