The upper open monophonic number of a graph

For a connected graph G of order n,a subset S of vertices of G is a monophonic set of G if each vertex v in G lies on a x-y monophonic path for some elements x and y in S. The minimum cardinality of a monophonic set of G is defined as the monophonic number of G, denoted by m(G). A monophonic set of...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Santhakumaran,A. P., Mahendran,M.
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2014
Materias:	Distance geodesic geodetic number open geodetic number monophonic number open monophonic number upper open monophonic number
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172014000400003
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:scielo:S0716-09172014000400003
record_format	dspace
spelling	oai:scielo:S0716-091720140004000032015-01-19The upper open monophonic number of a graphSanthakumaran,A. P.Mahendran,M. Distance geodesic geodetic number open geodetic number monophonic number open monophonic number upper open monophonic number For a connected graph G of order n,a subset S of vertices of G is a monophonic set of G if each vertex v in G lies on a x-y monophonic path for some elements x and y in S. The minimum cardinality of a monophonic set of G is defined as the monophonic number of G, denoted by m(G). A monophonic set of cardinality m(G) is called a m-set of G.A set S of vertices of a connected graph G is an open monophonic set of G if for each vertex v in G ,either v is an extreme vertex of G and v G S,or v is an internal vertex of a x-y mono-phonic path for some x,y G S. An open monophonic set of minimum cardinality is a minimum open monophonic set and this cardinality is the open monophonic number, om(G). An open monophonic set S of vertices in a connected graph G is a minimal open monophonic .set if no proper subset of S is an open monophonic set of G.The upper open monophonic number om+ (G) is the maximum cardinality of a minimal open monophonic set of G. The upper open monophonic numbers of certain standard graphs are determined. It is proved that for a graph G of order n, om(G) = n if and only if om+(G)= n. Graphs G with om(G) = 2 are characterized. If a graph G has a minimal open monophonic set S of cardinality 3, then S is also a minimum open monophonic set of G and om(G) = 3. For any two positive integers a and b with 4 < a < b, there exists a connected graph G with om(G) = a and om+(G) = b.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.33 n.4 20142014-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172014000400003en10.4067/S0716-09172014000400003
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Distance geodesic geodetic number open geodetic number monophonic number open monophonic number upper open monophonic number
spellingShingle	Distance geodesic geodetic number open geodetic number monophonic number open monophonic number upper open monophonic number Santhakumaran,A. P. Mahendran,M. The upper open monophonic number of a graph
description	For a connected graph G of order n,a subset S of vertices of G is a monophonic set of G if each vertex v in G lies on a x-y monophonic path for some elements x and y in S. The minimum cardinality of a monophonic set of G is defined as the monophonic number of G, denoted by m(G). A monophonic set of cardinality m(G) is called a m-set of G.A set S of vertices of a connected graph G is an open monophonic set of G if for each vertex v in G ,either v is an extreme vertex of G and v G S,or v is an internal vertex of a x-y mono-phonic path for some x,y G S. An open monophonic set of minimum cardinality is a minimum open monophonic set and this cardinality is the open monophonic number, om(G). An open monophonic set S of vertices in a connected graph G is a minimal open monophonic .set if no proper subset of S is an open monophonic set of G.The upper open monophonic number om+ (G) is the maximum cardinality of a minimal open monophonic set of G. The upper open monophonic numbers of certain standard graphs are determined. It is proved that for a graph G of order n, om(G) = n if and only if om+(G)= n. Graphs G with om(G) = 2 are characterized. If a graph G has a minimal open monophonic set S of cardinality 3, then S is also a minimum open monophonic set of G and om(G) = 3. For any two positive integers a and b with 4 < a < b, there exists a connected graph G with om(G) = a and om+(G) = b.
author	Santhakumaran,A. P. Mahendran,M.
author_facet	Santhakumaran,A. P. Mahendran,M.
author_sort	Santhakumaran,A. P.
title	The upper open monophonic number of a graph
title_short	The upper open monophonic number of a graph
title_full	The upper open monophonic number of a graph
title_fullStr	The upper open monophonic number of a graph
title_full_unstemmed	The upper open monophonic number of a graph
title_sort	upper open monophonic number of a graph
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2014
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172014000400003
work_keys_str_mv	AT santhakumaranap theupperopenmonophonicnumberofagraph AT mahendranm theupperopenmonophonicnumberofagraph AT santhakumaranap upperopenmonophonicnumberofagraph AT mahendranm upperopenmonophonicnumberofagraph
_version_	1718439800894128128

The upper open monophonic number of a graph

Ejemplares similares