Fractional eternal domination: securely distributing resources across a network

04/24/2023
by   Fnu Devvrit, et al.
0

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.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset