Forcing Independent Spectrum in Graphs

Let G = (V, E) be a simple graph. Let S be a maximum independent set of G. A subset T of S is called a forcing subset if T is contained in no other maximum independent subset in G. The independent forcing number of S denoted by fI(G, S) is the cardinality of a minimum forcing subset of S. The independent forcing number of G is the minimum of the independent forcing number of S, where S is a maximum independent subset in G. The independent forcing spectrum of G denoted by SpecI(G) is defined as the set SpecI(G) = {k : there exists a maximum independent set S of G such that fI(G, S) = k}. In this paper, a study of SpecI(G) is made..