Javier Hassan

Super Zero Forcing in Some Graphs.

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...

2-Distance Certified Independence in the Join of Two Graphs.

Given a simple and undirected graph G=(V(G),E(G)). Then R\subseteq V(G) is called a 2-distance certified independent set of G if R satisfies the following two conditions:(i)For every x\in R, x has either zero or at least two hop neighborhood in V(G)\setminus R; and (ii) R is an independent set of G. The 2-distance cer...

A New Variant of HOP Independence.

Let G=(V(G), E(G)) be a simple and undirected graph. Then P \subseteq V(G) is called a 2-distance certified hop independent set of G if P is a hop independent and for every vertex v in P, v has either zero or at least two hop neighbors in V(G) \setminus P. The 2-distance certified hop independence number of G, denoted...

2-Distance Certified Independence in the Join of Two Graphs