The Strong Total Roman Domination in Fuzzy Graphs

Document Type : Original paper

Authors

1 Departamento de Matemática Aplicada I, Universidad de Sevilla, Spain

2 Departamento de Matemáticas, Universidad de Cádiz, Algeciras Campus, Spain

Abstract

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.

Keywords

Main Subjects

References

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Communications in Combinatorics and Optimization
Volume 11, Issue 4
Special issue in honor of Prof. Odile Favaron
December 2026
Pages 1333-1357

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