Connected edge monophonic number of a graph

For a connected graph G of order n,a set S of vertices is called an edge monophonic set of G if every edge of G lies on a monophonic path joining some pair of vertices in S, and the edge monophonic number m e(G) is the minimum cardinality of an edge monophonic set. An edge monophonic set S of G is a...

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Autores principales:	Santhakumaran,A P, Titus,P., Balakrishnan,P.
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2013
Materias:	Monophonic path edge monophonic number connected edge monophonic number connected edge geodetic number
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172013000300002
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spelling	oai:scielo:S0716-091720130003000022013-09-02Connected edge monophonic number of a graphSanthakumaran,A PTitus,P.Balakrishnan,P. Monophonic path edge monophonic number connected edge monophonic number connected edge geodetic number For a connected graph G of order n,a set S of vertices is called an edge monophonic set of G if every edge of G lies on a monophonic path joining some pair of vertices in S, and the edge monophonic number m e(G) is the minimum cardinality of an edge monophonic set. An edge monophonic set S of G is a connected edge mono-phonic set if the subgraph induced by S is connected, and the connected edge monophonic number m ce(G) is the minimum cardinality of a connected edge monophonic set of G. Graphs of order n with connected edge monophonic number 2, 3 or n are characterized. It is proved that there is no non-complete graph G of order n > 3 with m e(G) = 3 and m ce(G)= 3. It is shown that for integers k,l and n with 4 < k < l < n, there exists a connected graph G of order n such that m e(G) = k and m ce(G) = l.Also, for integers j,k and l with 4 < j < k < l, there exists a connected graph G such that m e(G)= j,m ce(G)= k and g ce(G) = l,where g ce(G) is the connected edge geodetic number ofa graph G.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.32 n.3 20132013-09-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172013000300002en10.4067/S0716-09172013000300002
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Monophonic path edge monophonic number connected edge monophonic number connected edge geodetic number
spellingShingle	Monophonic path edge monophonic number connected edge monophonic number connected edge geodetic number Santhakumaran,A P Titus,P. Balakrishnan,P. Connected edge monophonic number of a graph
description	For a connected graph G of order n,a set S of vertices is called an edge monophonic set of G if every edge of G lies on a monophonic path joining some pair of vertices in S, and the edge monophonic number m e(G) is the minimum cardinality of an edge monophonic set. An edge monophonic set S of G is a connected edge mono-phonic set if the subgraph induced by S is connected, and the connected edge monophonic number m ce(G) is the minimum cardinality of a connected edge monophonic set of G. Graphs of order n with connected edge monophonic number 2, 3 or n are characterized. It is proved that there is no non-complete graph G of order n > 3 with m e(G) = 3 and m ce(G)= 3. It is shown that for integers k,l and n with 4 < k < l < n, there exists a connected graph G of order n such that m e(G) = k and m ce(G) = l.Also, for integers j,k and l with 4 < j < k < l, there exists a connected graph G such that m e(G)= j,m ce(G)= k and g ce(G) = l,where g ce(G) is the connected edge geodetic number ofa graph G.
author	Santhakumaran,A P Titus,P. Balakrishnan,P.
author_facet	Santhakumaran,A P Titus,P. Balakrishnan,P.
author_sort	Santhakumaran,A P
title	Connected edge monophonic number of a graph
title_short	Connected edge monophonic number of a graph
title_full	Connected edge monophonic number of a graph
title_fullStr	Connected edge monophonic number of a graph
title_full_unstemmed	Connected edge monophonic number of a graph
title_sort	connected edge 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=S0716-09172013000300002
work_keys_str_mv	AT santhakumaranap connectededgemonophonicnumberofagraph AT titusp connectededgemonophonicnumberofagraph AT balakrishnanp connectededgemonophonicnumberofagraph
_version_	1718439791097282560

Connected edge monophonic number of a graph

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