Kernelization and lower bounds of the signed domination problem

Abstract

A function f: V → { - 1, + 1} defined on the vertex set of a graph G = (V, E) is a signed dominating function if the sum of its function values over the closed neighborhood of every vertex is positive. A signed dominating set of a graph G (with respect to a signed dominating function f) is the set of vertices in G that are assigned value + 1 by f. The minimum signed dominating set problem has important applications in the study of social networks. In this paper, we present a general technique that can be used to obtain kernels for the signed dominating set problem on various graphs. Our kernelization results also lead to strong and tight lower bounds on the size of minimum signed dominating sets and signed domination numbers for many graph classes. © 2013 Springer-Verlag Berlin Heidelberg.