Edge fixed monophonic number of a graph

Abstract: For an edge xy in a connected graph G of order p ≥ 3, a set S V(G)is an xy-monophonic set of G if each vertex v Є V(G) lies on an x-u monophonic path or a y-u monophonic path for some element u in S. The minimum cardinality of an xy- monophonic set of G is defined as th...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Titus,P., Vanaja,S. Eldin
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2017
Materias:	Monophonic path vertex monophonic number edge fixed monophonic number
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000300363
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:scielo:S0716-09172017000300363
record_format	dspace
spelling	oai:scielo:S0716-091720170003003632017-10-31Edge fixed monophonic number of a graphTitus,P.Vanaja,S. Eldin Monophonic path vertex monophonic number edge fixed monophonic number Abstract: For an edge xy in a connected graph G of order p ≥ 3, a set S V(G)is an xy-monophonic set of G if each vertex v Є V(G) lies on an x-u monophonic path or a y-u monophonic path for some element u in S. The minimum cardinality of an xy- monophonic set of G is defined as the xy-monophonic number of G, denoted by mxy (G) . An xy-monophonic set of cardinality mxy (G) is called a mxy -set of G. We determine bounds for it and find the same for special classes of graphs. It is shown that for any three positive integers r, d and n ≥ 2 with 2 ≤ r ≤ d, there exists a connected graph G with monophonic radius r, monophonic diameter d and mxy (G) = n for some edge xy in G.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.36 n.3 20172017-09-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000300363en10.4067/S0716-09172017000300363
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Monophonic path vertex monophonic number edge fixed monophonic number
spellingShingle	Monophonic path vertex monophonic number edge fixed monophonic number Titus,P. Vanaja,S. Eldin Edge fixed monophonic number of a graph
description	Abstract: For an edge xy in a connected graph G of order p ≥ 3, a set S V(G)is an xy-monophonic set of G if each vertex v Є V(G) lies on an x-u monophonic path or a y-u monophonic path for some element u in S. The minimum cardinality of an xy- monophonic set of G is defined as the xy-monophonic number of G, denoted by mxy (G) . An xy-monophonic set of cardinality mxy (G) is called a mxy -set of G. We determine bounds for it and find the same for special classes of graphs. It is shown that for any three positive integers r, d and n ≥ 2 with 2 ≤ r ≤ d, there exists a connected graph G with monophonic radius r, monophonic diameter d and mxy (G) = n for some edge xy in G.
author	Titus,P. Vanaja,S. Eldin
author_facet	Titus,P. Vanaja,S. Eldin
author_sort	Titus,P.
title	Edge fixed monophonic number of a graph
title_short	Edge fixed monophonic number of a graph
title_full	Edge fixed monophonic number of a graph
title_fullStr	Edge fixed monophonic number of a graph
title_full_unstemmed	Edge fixed monophonic number of a graph
title_sort	edge fixed monophonic number of a graph
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2017
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000300363
work_keys_str_mv	AT titusp edgefixedmonophonicnumberofagraph AT vanajaseldin edgefixedmonophonicnumberofagraph
_version_	1718439824241721344

Edge fixed monophonic number of a graph

Ejemplares similares