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Mixed double Roman domination in graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 12، دوره 11، شماره 2، شهریور 2026، صفحه 503-519 اصل مقاله (522.51 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.28947.1789 | ||
| نویسندگان | ||
| H. Abdollahzadeh Ahangar* 1؛ M. Chellali2؛ S.M. Sheikholeslami3؛ J.C. Valenzuela Tripodoro4 | ||
| 1Department of Mathematics, Babol Noshirvani University of Technology, Shariati Ave., Babol, I.R. Iran, Postal Code: 47148-71167 | ||
| 2LAMDA-RO Laboratory, Department of Mathematics, University of Blida, Blida, Algeria | ||
| 3Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran | ||
| 4Department of Mathematics, University of Cádiz, Spain | ||
| چکیده | ||
| Let $G=(V,E)$ be a simple graph with vertex set $V$ and edge set $E$. A mixed double Roman dominating function (MDRDF) of $G$ is a function $f:V\cup E \rightarrow \{0,1,2,3\}$ satisfying (1) for any element $x\in V\cup E$ with $f(x)=0$, there must be either element $y\in V\cup E$, with $f(y)=3,$ which is adjacent or incident to $x$, or either two elements $y,z \in V\cup E$, with $f(y),f(z)=2$ which are adjacent or incident to $x$; (2) for any element $x\in V\cup E$ with $f(x)=1$, there must be either element $y\in V\cup E$, with $f(y)\ge 2,$ which is adjacent or incident to $x$. The weight of an MDRDF $f$ is $w(f)=f(V\cup E)=\sum_{x\in V\cup E} f(x)$ and the minimum weight among all the MDRD functions the \textit{MDRD-number}, $\gamma _{dR}^*(G)$, of the graph $G$. In this paper we start the study of this variation of the classic Roman domination problem by setting some basic results, giving exact values and sharp bounds of the MDRD number and we approach the study of the complexity of the decision problem associated to the MDR domination in graphs. | ||
| کلیدواژهها | ||
| Roman domination, double Roman domination؛ mixed double Roman domination | ||
| مراجع | ||
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