This paper studies total domination in interval-valued neutrosophic graphs $ (IVN_{graphs}) $, which extend classical graph structures by associating each node and edge with interval-valued degrees of truth, indeterminacy, and falsity. The main objective of this study is to generalize the concept of total domination from single-valued neutrosophic graphs to the interval-valued framework. We introduce formal definitions related to total domination and derive key conditions and properties of total dominating sets. An illustrative example is provided to support the theoretical developments and to demonstrate the applicability of the proposed framework. Extending the traditional domination theory to the interval-valued neutrosophic domain provides a more flexible and realistic model for handling uncertainties in complex network systems and offers a methodological foundation for further research in neutrosophic graph theory.
Citation: T. P. Sreelakshmi, K. Uma Samundesvari. Total domination concepts in interval-valued neutrosophic graphs[J]. AIMS Mathematics, 2026, 11(6): 15435-15447. doi: 10.3934/math.2026634
This paper studies total domination in interval-valued neutrosophic graphs $ (IVN_{graphs}) $, which extend classical graph structures by associating each node and edge with interval-valued degrees of truth, indeterminacy, and falsity. The main objective of this study is to generalize the concept of total domination from single-valued neutrosophic graphs to the interval-valued framework. We introduce formal definitions related to total domination and derive key conditions and properties of total dominating sets. An illustrative example is provided to support the theoretical developments and to demonstrate the applicability of the proposed framework. Extending the traditional domination theory to the interval-valued neutrosophic domain provides a more flexible and realistic model for handling uncertainties in complex network systems and offers a methodological foundation for further research in neutrosophic graph theory.
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T. P. Sreelakshmi, K. Uma Samundesvari. Total domination concepts in interval-valued neutrosophic graphs[J]. AIMS Mathematics, 2026, 11(6): 15435-15447. doi: 10.3934/math.2026634
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