Zero Forcing Number and Maximum Nullity of General Power Graphs

Document Type : Original Manuscript

Authors

1 Imam Khomeini International University

2 Department of Pure Mathematics Faculty of Basic Science Imam Khomeini International University

Abstract

Let Γ = (V,E) be a simple and undirected graph. General power graph of Γ, shown by Pg(Γ), is a graph with the vertex set P(V (Γ))\ϕ. Also two distinct vertices of B and C are adjacent if and only if every b ∈ B is adjacent to every c ∈ C \{b} in Γ. In this paper, we consider general power graph related to graph Γ. Also we show that zero forcing number is equal to maximum nullity, for general power graph of some graphs.

Keywords