Zero forcing in Benzenoid network

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 p...

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Autores principales:	Anitha,J., Rajasingh,Indra
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2019
Materias:	Zero forcing set Pyrene networks Circum-pyrene networks Circum-trizene networks.
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000500999
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spelling	oai:scielo:S0716-091720190005009992020-01-07Zero forcing in Benzenoid networkAnitha,J.Rajasingh,Indra Zero forcing set Pyrene networks Circum-pyrene networks Circum-trizene networks. 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.38 n.5 20192019-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000500999en10.22199/issn.0717-6279-2019-05-0064
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Zero forcing set Pyrene networks Circum-pyrene networks Circum-trizene networks.
spellingShingle	Zero forcing set Pyrene networks Circum-pyrene networks Circum-trizene networks. Anitha,J. Rajasingh,Indra Zero forcing in Benzenoid network
description	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.
author	Anitha,J. Rajasingh,Indra
author_facet	Anitha,J. Rajasingh,Indra
author_sort	Anitha,J.
title	Zero forcing in Benzenoid network
title_short	Zero forcing in Benzenoid network
title_full	Zero forcing in Benzenoid network
title_fullStr	Zero forcing in Benzenoid network
title_full_unstemmed	Zero forcing in Benzenoid network
title_sort	zero forcing in benzenoid network
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2019
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000500999
work_keys_str_mv	AT anithaj zeroforcinginbenzenoidnetwork AT rajasinghindra zeroforcinginbenzenoidnetwork
_version_	1718439860616822784

Zero forcing in Benzenoid network

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