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The Strong Total Roman Domination in Fuzzy Graphs | ||
| Communications in Combinatorics and Optimization | ||
| دوره 11، شماره 4، اسفند 2026، صفحه 1333-1357 اصل مقاله (615.58 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.31398.2841 | ||
| نویسندگان | ||
| Martin Cera1؛ Pedro Garcia-Vazquez1؛ Juan Carlos Valenzuela Tripodoro* 2 | ||
| 1Departamento de Matemática Aplicada I, Universidad de Sevilla, Spain | ||
| 2Departamento de Matemáticas, Universidad de Cádiz, Algeciras Campus, Spain | ||
| چکیده | ||
| In recent years, domination theory and its variants, including Roman domination, have been widely studied in fuzzy graphs due to their ability to model uncertainty in complex networks such as social, transportation, and biological systems. A strong total Roman dominating function (STRDF) on a fuzzy graph $G=(V,\sigma,\mu)$ is a mapping $f:V\rightarrow \{0,1,2\}$ such that every vertex $u$ with $f(u)=0$ has a strong neighbor labeled 2, and every vertex labeled 1 or 2 has at least one strong neighbor with a non-zero label. The strong total Roman domination number, $\gamma_{sR}^t(G)$, is defined as the minimum weight $\sum_{u\in V} f(u)\mu_s(u)$ among all STRDFs $f,$ where $\mu_s(u)$ denotes the minimum membership value of the strong edges incident to $u$. In this paper, we introduce and study the strong total Roman domination number for fuzzy graphs. We establish several bounds, investigate its realizability, determine exact values for several standard families of fuzzy graphs, and present some applications. | ||
| کلیدواژهها | ||
| Domination؛ total Roman domination؛ fuzzy graphs | ||
| مراجع | ||
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