On the upper geodetic global domination number of a graph

Abstract A set S of vertices in a connected graph G = (V, E) is called a geodetic set if every vertex not in S lies on a shortest path between two vertices from S. A set D of vertices in G is called a dominating set of G if every vertex not in D has at least one neighbor in D. A set D is called a gl...

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Autores principales:	Lenin Xaviour,X., Robinson Chellathurai,S.
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2020
Materias:	Geodetic set Dominating set Geodetic domination Geodetic global domination Upper geodetic global domination number
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000601627
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spelling	oai:scielo:S0716-091720200006016272020-12-02On the upper geodetic global domination number of a graphLenin Xaviour,X.Robinson Chellathurai,S. Geodetic set Dominating set Geodetic domination Geodetic global domination Upper geodetic global domination number Abstract A set S of vertices in a connected graph G = (V, E) is called a geodetic set if every vertex not in S lies on a shortest path between two vertices from S. A set D of vertices in G is called a dominating set of G if every vertex not in D has at least one neighbor in D. A set D is called a global dominating set in G if S is a dominating set of both G and Ḡ. A set S is called a geodetic global dominating set of G if S is both geodetic and global dominating set of G. A geodetic global dominating set S in G is called a minimal geodetic global dominating set if no proper subset of S is itself a geodetic global dominating set in G. The maximum cardinality of a minimal geodetic global dominating set in G is the upper geodetic global domination number Ῡg +(G) of G. In this paper, the upper geodetic global domination number of certain connected graphs are determined and some of the general properties are studied. It is proved that for all positive integers a, b, p where 3 ≤ a ≤ b < p, there exists a connected graph G such that Ῡg(G) = a, Ῡg +(G) = b and \|V (G)\| = p.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.39 n.6 20202020-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000601627en10.22199/issn.0717-6279-2020-06-0097
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Geodetic set Dominating set Geodetic domination Geodetic global domination Upper geodetic global domination number
spellingShingle	Geodetic set Dominating set Geodetic domination Geodetic global domination Upper geodetic global domination number Lenin Xaviour,X. Robinson Chellathurai,S. On the upper geodetic global domination number of a graph
description	Abstract A set S of vertices in a connected graph G = (V, E) is called a geodetic set if every vertex not in S lies on a shortest path between two vertices from S. A set D of vertices in G is called a dominating set of G if every vertex not in D has at least one neighbor in D. A set D is called a global dominating set in G if S is a dominating set of both G and Ḡ. A set S is called a geodetic global dominating set of G if S is both geodetic and global dominating set of G. A geodetic global dominating set S in G is called a minimal geodetic global dominating set if no proper subset of S is itself a geodetic global dominating set in G. The maximum cardinality of a minimal geodetic global dominating set in G is the upper geodetic global domination number Ῡg +(G) of G. In this paper, the upper geodetic global domination number of certain connected graphs are determined and some of the general properties are studied. It is proved that for all positive integers a, b, p where 3 ≤ a ≤ b < p, there exists a connected graph G such that Ῡg(G) = a, Ῡg +(G) = b and \|V (G)\| = p.
author	Lenin Xaviour,X. Robinson Chellathurai,S.
author_facet	Lenin Xaviour,X. Robinson Chellathurai,S.
author_sort	Lenin Xaviour,X.
title	On the upper geodetic global domination number of a graph
title_short	On the upper geodetic global domination number of a graph
title_full	On the upper geodetic global domination number of a graph
title_fullStr	On the upper geodetic global domination number of a graph
title_full_unstemmed	On the upper geodetic global domination number of a graph
title_sort	on the upper geodetic global domination number of a graph
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2020
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000601627
work_keys_str_mv	AT leninxaviourx ontheuppergeodeticglobaldominationnumberofagraph AT robinsonchellathurais ontheuppergeodeticglobaldominationnumberofagraph
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On the upper geodetic global domination number of a graph

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