Edge Detour Monophonic Number of a Graph

For a connected graph G of order at least two, an edge detour monophonic set of G is a set S of vertices such that every edge of G lies on a detour monophonic path joining some pair of vertices in S. The edge detour monophonic number of G is the minimum cardinality of its edge detour monophonic sets...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Santhakumaran,A. P., Titus,P, Ganesamoorthy,K, Balakrishnan,P
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2013
Materias:	monophonic number edge monophonic number detour monophonic number edge detour monophonic number
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172013000200007
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:scielo:S0716-09172013000200007
record_format	dspace
spelling	oai:scielo:S0716-091720130002000072013-06-26Edge Detour Monophonic Number of a GraphSanthakumaran,A. P.Titus,PGanesamoorthy,KBalakrishnan,P monophonic number edge monophonic number detour monophonic number edge detour monophonic number For a connected graph G of order at least two, an edge detour monophonic set of G is a set S of vertices such that every edge of G lies on a detour monophonic path joining some pair of vertices in S. The edge detour monophonic number of G is the minimum cardinality of its edge detour monophonic sets and is denoted by edm(G) .We determine bounds for it and characterize graphs which realize these bounds. Also, certain general properties satisfied by an edge detour monophonic set are studied. It is shown that for positive integers a, b and c with 2 ≤ a ≤ c, there exists a connected graph G such that m(G) = a, m!(G) = b and edm(G) = c,where m(G) is the monophonic number and m! (G) is the edge monophonic number of G. Also, for any integers a and b with 2 ≤ a ≤ b, there exists a connected graph G such that dm(G) = a and edm(G)= b,where dm(G) is the detour monophonic number of a graph G.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.32 n.2 20132013-05-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172013000200007en10.4067/S0716-09172013000200007
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	monophonic number edge monophonic number detour monophonic number edge detour monophonic number
spellingShingle	monophonic number edge monophonic number detour monophonic number edge detour monophonic number Santhakumaran,A. P. Titus,P Ganesamoorthy,K Balakrishnan,P Edge Detour Monophonic Number of a Graph
description	For a connected graph G of order at least two, an edge detour monophonic set of G is a set S of vertices such that every edge of G lies on a detour monophonic path joining some pair of vertices in S. The edge detour monophonic number of G is the minimum cardinality of its edge detour monophonic sets and is denoted by edm(G) .We determine bounds for it and characterize graphs which realize these bounds. Also, certain general properties satisfied by an edge detour monophonic set are studied. It is shown that for positive integers a, b and c with 2 ≤ a ≤ c, there exists a connected graph G such that m(G) = a, m!(G) = b and edm(G) = c,where m(G) is the monophonic number and m! (G) is the edge monophonic number of G. Also, for any integers a and b with 2 ≤ a ≤ b, there exists a connected graph G such that dm(G) = a and edm(G)= b,where dm(G) is the detour monophonic number of a graph G.
author	Santhakumaran,A. P. Titus,P Ganesamoorthy,K Balakrishnan,P
author_facet	Santhakumaran,A. P. Titus,P Ganesamoorthy,K Balakrishnan,P
author_sort	Santhakumaran,A. P.
title	Edge Detour Monophonic Number of a Graph
title_short	Edge Detour Monophonic Number of a Graph
title_full	Edge Detour Monophonic Number of a Graph
title_fullStr	Edge Detour Monophonic Number of a Graph
title_full_unstemmed	Edge Detour Monophonic Number of a Graph
title_sort	edge detour monophonic number of a graph
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2013
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172013000200007
work_keys_str_mv	AT santhakumaranap edgedetourmonophonicnumberofagraph AT titusp edgedetourmonophonicnumberofagraph AT ganesamoorthyk edgedetourmonophonicnumberofagraph AT balakrishnanp edgedetourmonophonicnumberofagraph
_version_	1718439790613889024

Edge Detour Monophonic Number of a Graph

Ejemplares similares