Upper double monophonic number of a graph

Abstract: A set S of a connected graph G of order n is called a double monophonic set of G if for every pair of vertices x, y in G there exist vertices u, v in S such that x, y lie on a u-v monophonic path. The double monophonic number dm(G) of G is the minimum cardinality of a double monophonic set...

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Autores principales:	Santhakumaran,A. P., Raghu,T. Venkata
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2018
Materias:	Double monophonic set double monophonic number upper double monophonic set upper double monophonic number
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000200295
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spelling	oai:scielo:S0716-091720180002002952018-05-29Upper double monophonic number of a graphSanthakumaran,A. P.Raghu,T. Venkata Double monophonic set double monophonic number upper double monophonic set upper double monophonic number Abstract: A set S of a connected graph G of order n is called a double monophonic set of G if for every pair of vertices x, y in G there exist vertices u, v in S such that x, y lie on a u-v monophonic path. The double monophonic number dm(G) of G is the minimum cardinality of a double monophonic set. A double monophonic set S in a connected graph G is called a minimal double monophonic set if no proper subset of S is a double monophonic set of G. The upper double monophonic number of G is the maximum cardinality of a minimal double monophonic set of G, and is denoted by dm+(G). Some general properties satisfied by upper double monophonic sets are discussed. It is proved that for a connected graph G of order n, dm(G)=n if and only if dm+(G)=n. It is also proved that dm(G)=n-1 if and only if dm+(G)=n-1 for a non-complete graph G of order n with a full degree vertex. For any positive integers 2 ≤ a ≤ b, there exists a connected graph G with dm(G)= a and dm+(G)=b.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.37 n.2 20182018-06-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000200295en10.4067/S0716-09172018000200295
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Double monophonic set double monophonic number upper double monophonic set upper double monophonic number
spellingShingle	Double monophonic set double monophonic number upper double monophonic set upper double monophonic number Santhakumaran,A. P. Raghu,T. Venkata Upper double monophonic number of a graph
description	Abstract: A set S of a connected graph G of order n is called a double monophonic set of G if for every pair of vertices x, y in G there exist vertices u, v in S such that x, y lie on a u-v monophonic path. The double monophonic number dm(G) of G is the minimum cardinality of a double monophonic set. A double monophonic set S in a connected graph G is called a minimal double monophonic set if no proper subset of S is a double monophonic set of G. The upper double monophonic number of G is the maximum cardinality of a minimal double monophonic set of G, and is denoted by dm+(G). Some general properties satisfied by upper double monophonic sets are discussed. It is proved that for a connected graph G of order n, dm(G)=n if and only if dm+(G)=n. It is also proved that dm(G)=n-1 if and only if dm+(G)=n-1 for a non-complete graph G of order n with a full degree vertex. For any positive integers 2 ≤ a ≤ b, there exists a connected graph G with dm(G)= a and dm+(G)=b.
author	Santhakumaran,A. P. Raghu,T. Venkata
author_facet	Santhakumaran,A. P. Raghu,T. Venkata
author_sort	Santhakumaran,A. P.
title	Upper double monophonic number of a graph
title_short	Upper double monophonic number of a graph
title_full	Upper double monophonic number of a graph
title_fullStr	Upper double monophonic number of a graph
title_full_unstemmed	Upper double monophonic number of a graph
title_sort	upper double monophonic number of a graph
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2018
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000200295
work_keys_str_mv	AT santhakumaranap upperdoublemonophonicnumberofagraph AT raghutvenkata upperdoublemonophonicnumberofagraph
_version_	1718439834614235136

Upper double monophonic number of a graph

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