Year: 2026
Type: article
Abstract: Objective: This study provides the fractional double domination number of a graph and analyses its essential aspects. Method: A fractional double dominating function of a graph πΊ = (π , πΈ) is defined as a function π βΆ π β [0, 1] such that Ξ£π’βπ[π£] π(π’) β₯ 2 for every vertex π£ β π , where π[π£] denotes the closed neighborhood of π£. The fractional double domination number, denoted by πΎππ(πΊ), is the minimum weight Ξ£π£βπ π(π£) taken over all such functions. Findings: This study establishes general bounds for πΎππ(πΊ) and derives exact values for several standard classes of graphs including paths, cycles, stars, wheels, and complete graphs. Furthermore, the analysis is extended to dual graphs, presenting new bounds and relationships between the fractional double domination numbers of a graph and its dual. Illustrative examples and constructive assignments are provided to demonstrate the tightness of the bounds. Novelty: The results presented herein not only broaden the scope of fractional domination theory but also contribute to the growing body of research on domination parameters with redundancy and robustness in networks. Keywords: Fractional Domination Number; Fractional double domination; Dual graphs; Bounds
Authors: B Vembu, M Kalaiselvi
Institution: Manonmaniam Sundaranar University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7133132186
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