Some properties of the closed global shadow graphs and their zero forcing number

Abstract

Zero forcing is one of the dynamic vertex coloring problem. Zero forcing number is the minimum cardinality of the zero forcing sets. This parameter is the upper bound for the maximum nullity. A new class of graph where the maximum nullity is equal to the zero forcing number of the graph is defined as closed global shadow graph. Basic properties and zero forcing number of this graph class is analysed.

Keywords

• zero forcing number
• zero forcing set
• closed global shadow graph
• open global shadow graph
• 05c07
• 05c38
• 05c50
• 05c69