Fractional eternal domination: securely distributing resources across a network

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 gamma f infinity(G). We study the behaviour of gamma f infinity (G) as it relates to other domination parameters. We also determine bounds on, and in some cases exact values for, gamma f infinity (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.