Super Zero Forcing in Some Graphs.

Abstract

Let G=(V(G), E(G)) be a simple and undirected graph. Then I \subseteq V(G) is called a Super Zero Forcing Set of G, if I satisfies (i). I is a zero forcing set of G, and (ii). I is a super set of G; that is, for every x in V(G) \setminus I, there exists y in I such that (V(G)\setminus I)\capN_G(y)=\{x\}. The Super Zero Forcing Number of G, denoted by Z_s(G), is the minimum cardinality of a super zero forcing set of G. In this paper, we introduce this concept and investigate its properties on some special graphs such as complete, path, cycle, and edgeless graph. Moreover, we present some formulas and characterizations of this new concept.