Open global shadow graph and its zero forcing number
Open global shadow graph; Zero forcing number; Zero forcing set
Zero forcing number of a graph is the minimum cardinality of the zero forcing set. A zero forcing set is a set of black vertices of minimum cardinality that can colour the entire graph black using the colour change rule: each vertex of G is coloured either white or black, and vertex v is a black vertex and can force a white neighbour only if it has one white neighbour. In this paper we identify a class of graph where the zero forcing number is equal to the minimum rank of the graph and call it as a new class of graph that is open global shadow graph. Some of the basic properties of open global shadow graph are studied. The zero forcing number of open global shadow graph of a graph with upper and lower bound is obtained. Hence giving the upper and lower bound for the minimum rank of the graph. 2023, Proyecciones. All Rights Reserved.
All Open Access; Gold Open Access; Green Open Access
Raksha M.R., CHRIST (Deemed to be University), India; Dominic C., CHRIST (Deemed to be University), India