Bounds on the forcing domination number of graphs

Abstract

A set S of vertices is a dominating set if (V \S) ⊆ N(S), or equivalently, every vertex in V \S has a neighbor in S. A subset T of a minimum dominating set S of G is called a forcing subset for S if S is the unique minimum dominating set containing T. The forcing domination number f(S, γ) of S is the minimum cardinality of a forcing subset for S. The forcing domination number f(G, γ) of G is the smallest forcing number of a minimum dominating set of G. In this paper we present some sharp bounds on the forcing domination number.