Zero forcing in Benzenoid network

• Published in: Proyecciones (Antofagasta) Vol. 38; no. 5; pp. 999 - 1010
• Main Authors: Anitha, J., Rajasingh, Indra
• Format: Journal Article
• Language: English; Portuguese
• Published: Universidad Católica del Norte, Departamento de Matemáticas 01.12.2019
• Subjects: MATHEMATICS; Pyrene networks; Circum-pyrene networks; Circum-trizene networks; Zero forcing set
• ISSN: 0717-6279; 0716-0917; 0717-6279
• DOI: 10.22199/issn.0717-6279-2019-05-0064

Abstract A set S of vertices in a graph G is called a dominating set of G if every vertex in V (G)\S is adjacent to some vertex in S. A set S is said to be a power dominating set of G if every vertex in the system is monitored by the set S following a set of rules for power system monitoring. The power domination number of G is the minimum cardinality of a power dominating set of G. A dynamic coloring of the vertices of a graph G starts with an initial subset S of colored vertices, with all remaining vertices being non-colored. At each discrete time interval, a colored vertex with exactly one non-colored neighbor forces this non-colored neighbor to be colored. The initial set S is called a forcing set (zero forcing set) of G if, by iteratively applying the forcing process, every vertex in G becomes colored. The zero forcing number of G, denoted Z(G), is the minimum cardinality of a zero forcing set of G. In this paper, we obtain the zero forcing number for certain benzenoid networks.