Geodesic
Fractional eternal domination: securely distributing resources across a network
Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 4, pp. 1395-1428

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This paper initiates the study of fractional eternal domination in graphs, a natural relaxation of the well-studied eternal domination problem. We study the connections to flows and linear programming in order to obtain results on the complexity of determining the fractional eternal domination number of a graph G, which we denote γ_f^∞(G). We study the behaviour of γ_f^∞(G) as it relates to other domination parameters. We also determine bounds on, and in some cases exact values for, γ_f^∞(G) when G is a member of one of a variety of important graph classes, including trees, split graphs, strongly chordal graphs, Kneser graphs, abelian Cayley graphs, and graph products.
Keywords: eternal domination, fractional domination 
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     author = {Devvrit, Fnu and Krim-Yee, Aaron and Kumar, Nithish and MacGillivray, Gary and Seamone, Ben and Virgile, Virg\'elot and Xu, AnQi},
     title = {Fractional eternal domination: securely distributing resources across a network},
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Devvrit, Fnu; Krim-Yee, Aaron; Kumar, Nithish; MacGillivray, Gary; Seamone, Ben; Virgile, Virgélot; Xu, AnQi. Fractional eternal domination: securely distributing resources across a network. Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 4, pp. 1395-1428. http://geodesic.mathdoc.fr/item/DMGT_2024_44_4_a9/