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- Title
Open global shadow graph and it's zero forcing number.
- Authors
Raksha, M. R.; Dominic, Charles
- Abstract
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.
- Subjects
COLOR; ZERO (The number)
- Publication
Proyecciones - Journal of Mathematics, 2023, Vol 42, Issue 1, p33
- ISSN
0716-0917
- Publication type
Article
- DOI
10.22199/issn.0717-6279-5305