Edge-to-vertex m-detour monophonic number of a graph

Abstract For a connected graph G = (V, E) of order at least three, the monophonic distance dm(u, v) is the length of a longest u − v monophonic path in G. A u − v path of length dm(u, v) is called a u − v detour monophonic. For subsets A and B of V, the m-monophonic dis...

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Autores principales:	Santhakumaran,A. P., Titus,P., Ganesamoorthy,K.
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2018
Materias:	monophonic distance m-detour monophonic path edge-to-vertex m-detour monophonic set edge-to-vertex m-detour monophonic basis edge-to-vertex m-detour monophonic number.
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000300415
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spelling	oai:scielo:S0716-091720180003004152018-10-10Edge-to-vertex m-detour monophonic number of a graphSanthakumaran,A. P.Titus,P.Ganesamoorthy,K. monophonic distance m-detour monophonic path edge-to-vertex m-detour monophonic set edge-to-vertex m-detour monophonic basis edge-to-vertex m-detour monophonic number. Abstract For a connected graph G = (V, E) of order at least three, the monophonic distance dm(u, v) is the length of a longest u − v monophonic path in G. A u − v path of length dm(u, v) is called a u − v detour monophonic. For subsets A and B of V, the m-monophonic distance Dm(A, B) is defined as Dm(A, B) = max{dm(x, y) : x ∈ A, y ∈ B}. A u − v path of length Dm(A, B) is called a A − B m-detour monophonic path joining the sets A, B ⊆ V, where u ∈ A and v ∈ B. A set S ⊆ E is called an edge-to-vertex m-detour monophonic set of G if every vertex of G is incident with an edge of S or lies on a m-detour monophonic path joining a pair of edges of S. The edge-to-vertex mdetour monophonic number Dmev(G) of G is the minimum order of its edge-to-vertex m-detour monophonic sets and any edge-to-vertex m-detour monophonic set of order Dmev(G) is an edge-to-vertex mdetour monophonic basis of G. Some general properties satisfied by this parameter are studied. The edge-to-vertex m-detour monophonic number of certain classes of graphs are determined. It is shown that for positive integers r, d and k ≥ 4 with r < d, there exists a connected graph G such that radm(G) = r, diamm(G) = d and Dmev(G) = k.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.37 n.3 20182018-09-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000300415en10.4067/S0716-09172018000300415
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	monophonic distance m-detour monophonic path edge-to-vertex m-detour monophonic set edge-to-vertex m-detour monophonic basis edge-to-vertex m-detour monophonic number.
spellingShingle	monophonic distance m-detour monophonic path edge-to-vertex m-detour monophonic set edge-to-vertex m-detour monophonic basis edge-to-vertex m-detour monophonic number. Santhakumaran,A. P. Titus,P. Ganesamoorthy,K. Edge-to-vertex m-detour monophonic number of a graph
description	Abstract For a connected graph G = (V, E) of order at least three, the monophonic distance dm(u, v) is the length of a longest u − v monophonic path in G. A u − v path of length dm(u, v) is called a u − v detour monophonic. For subsets A and B of V, the m-monophonic distance Dm(A, B) is defined as Dm(A, B) = max{dm(x, y) : x ∈ A, y ∈ B}. A u − v path of length Dm(A, B) is called a A − B m-detour monophonic path joining the sets A, B ⊆ V, where u ∈ A and v ∈ B. A set S ⊆ E is called an edge-to-vertex m-detour monophonic set of G if every vertex of G is incident with an edge of S or lies on a m-detour monophonic path joining a pair of edges of S. The edge-to-vertex mdetour monophonic number Dmev(G) of G is the minimum order of its edge-to-vertex m-detour monophonic sets and any edge-to-vertex m-detour monophonic set of order Dmev(G) is an edge-to-vertex mdetour monophonic basis of G. Some general properties satisfied by this parameter are studied. The edge-to-vertex m-detour monophonic number of certain classes of graphs are determined. It is shown that for positive integers r, d and k ≥ 4 with r < d, there exists a connected graph G such that radm(G) = r, diamm(G) = d and Dmev(G) = k.
author	Santhakumaran,A. P. Titus,P. Ganesamoorthy,K.
author_facet	Santhakumaran,A. P. Titus,P. Ganesamoorthy,K.
author_sort	Santhakumaran,A. P.
title	Edge-to-vertex m-detour monophonic number of a graph
title_short	Edge-to-vertex m-detour monophonic number of a graph
title_full	Edge-to-vertex m-detour monophonic number of a graph
title_fullStr	Edge-to-vertex m-detour monophonic number of a graph
title_full_unstemmed	Edge-to-vertex m-detour monophonic number of a graph
title_sort	edge-to-vertex m-detour 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=S0716-09172018000300415
work_keys_str_mv	AT santhakumaranap edgetovertexmdetourmonophonicnumberofagraph AT titusp edgetovertexmdetourmonophonicnumberofagraph AT ganesamoorthyk edgetovertexmdetourmonophonicnumberofagraph
_version_	1718439836728164352

Edge-to-vertex m-detour monophonic number of a graph

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