The total double geodetic number of a graph

Abstract For a connected graph G of order n, a set S of vertices is called a double geodetic set of G if for each pair of vertices x, y in G there exist vertices u, v ∈ S such that x, y ∈ I[u, v]. The double geodetic number dg(G) is the minimum cardinality of a double geodetic se...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Santhakumaran,A. P., Jebaraj,T.
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2020
Materias:	Geodetic number Double geodetic number Connected double geodetic number Total double geodetic number
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000100167
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:scielo:S0716-09172020000100167
record_format	dspace
spelling	oai:scielo:S0716-091720200001001672020-02-18The total double geodetic number of a graphSanthakumaran,A. P.Jebaraj,T. Geodetic number Double geodetic number Connected double geodetic number Total double geodetic number Abstract For a connected graph G of order n, a set S of vertices is called a double geodetic set of G if for each pair of vertices x, y in G there exist vertices u, v ∈ S such that x, y ∈ I[u, v]. The double geodetic number dg(G) is the minimum cardinality of a double geodetic set. Any double godetic set of cardinality dg(G) is called a dg-set of G. A connected double geodetic set of G is a double geodetic set S such that the subgraph G[S] induced by S is connected. The mínimum cardinality of a connected double geodetic set of G is the connected double geodetic number of G and is denoted by dgc(G). A connected double geodetic set of cardinality dgc(G) is called a dgc-set of G. A total double geodetic set of a graph G is a double geodetic set S such that the subgraph G[S] induced by S has no isolated vertices. The minimum cardinality of a total double geodetic set of G is the total double geodetic number of G and is denoted by dgt(G). For positive integers r, d and k ≥ 4 with r ≤ d ≤ 2r, there exists a connected graph G with rad G = r, diam G = d and dgt(G) = k. It is shown that if n, a, b are positive integers such that 4 ≤ a ≤ b ≤ n, then there exists a connected graph G of order n with dgt(G) = a and dgc(G) = b. Also, for integers a, b with 4 ≤ a ≤ b and b ≤ 2a, there exists a connected graph G such that dg(G) = a and dgt(G) = b.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.39 n.1 20202020-02-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000100167en10.22199/issn.0717-6279-2020-01-0011
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Geodetic number Double geodetic number Connected double geodetic number Total double geodetic number
spellingShingle	Geodetic number Double geodetic number Connected double geodetic number Total double geodetic number Santhakumaran,A. P. Jebaraj,T. The total double geodetic number of a graph
description	Abstract For a connected graph G of order n, a set S of vertices is called a double geodetic set of G if for each pair of vertices x, y in G there exist vertices u, v ∈ S such that x, y ∈ I[u, v]. The double geodetic number dg(G) is the minimum cardinality of a double geodetic set. Any double godetic set of cardinality dg(G) is called a dg-set of G. A connected double geodetic set of G is a double geodetic set S such that the subgraph G[S] induced by S is connected. The mínimum cardinality of a connected double geodetic set of G is the connected double geodetic number of G and is denoted by dgc(G). A connected double geodetic set of cardinality dgc(G) is called a dgc-set of G. A total double geodetic set of a graph G is a double geodetic set S such that the subgraph G[S] induced by S has no isolated vertices. The minimum cardinality of a total double geodetic set of G is the total double geodetic number of G and is denoted by dgt(G). For positive integers r, d and k ≥ 4 with r ≤ d ≤ 2r, there exists a connected graph G with rad G = r, diam G = d and dgt(G) = k. It is shown that if n, a, b are positive integers such that 4 ≤ a ≤ b ≤ n, then there exists a connected graph G of order n with dgt(G) = a and dgc(G) = b. Also, for integers a, b with 4 ≤ a ≤ b and b ≤ 2a, there exists a connected graph G such that dg(G) = a and dgt(G) = b.
author	Santhakumaran,A. P. Jebaraj,T.
author_facet	Santhakumaran,A. P. Jebaraj,T.
author_sort	Santhakumaran,A. P.
title	The total double geodetic number of a graph
title_short	The total double geodetic number of a graph
title_full	The total double geodetic number of a graph
title_fullStr	The total double geodetic number of a graph
title_full_unstemmed	The total double geodetic number of a graph
title_sort	total double geodetic 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=S0716-09172020000100167
work_keys_str_mv	AT santhakumaranap thetotaldoublegeodeticnumberofagraph AT jebarajt thetotaldoublegeodeticnumberofagraph AT santhakumaranap totaldoublegeodeticnumberofagraph AT jebarajt totaldoublegeodeticnumberofagraph
_version_	1718439865648939008

The total double geodetic number of a graph

Ejemplares similares