Characterization of Upper Detour Monophonic Domination Number

Abstract This paper introduces the concept of upper detour monophonic domination number of a graph. For a connected graph G with vertex set V (G), a set M ⊆ V (G) is called minimal detour monophonic dominating set, if no proper subset of M is a detour monophonic dominating set. The maximum...

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Autor principal:	Khayyoom,M. Mohammed Abdul
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2020
Materias:	Monophonic number Domination Number Detour monophonic number Detour monophonic domination number Upper detour monophonic domination number.
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462020000300315
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spelling	oai:scielo:S0719-064620200003003152020-12-30Characterization of Upper Detour Monophonic Domination NumberKhayyoom,M. Mohammed Abdul Monophonic number Domination Number Detour monophonic number Detour monophonic domination number Upper detour monophonic domination number. Abstract This paper introduces the concept of upper detour monophonic domination number of a graph. For a connected graph G with vertex set V (G), a set M ⊆ V (G) is called minimal detour monophonic dominating set, if no proper subset of M is a detour monophonic dominating set. The maximum cardinality among all minimal monophonic dominating sets is called upper detour monophonic domination number and is denoted by γ+ dm (G). For any two positive integers p and q with 2 ≤ p ≤ q there is a connected graph G with γm (G) = γdm (G) = p and γ+ dm (G) = q. For any three positive integers p, q, r with 2 < p < q < r, there is a connected graph G with m(G) = p, γdm (G) = q and γ+ dm (G) = r. Let p and q be two positive integers with 2 < p < q such that γdm (G) = p and γ+ dm (G) = q. Then there is a minimal DMD set whose cardinality lies between p and q. Let p, q and r be any three positive integers with 2 ≤ p ≤ q ≤ r. Then, there exist a connected graph G such that γm (G)= p, γ+ dm (G) = q and \|V (G)\| = r.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.22 n.3 20202020-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462020000300315en10.4067/S0719-06462020000300315
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Monophonic number Domination Number Detour monophonic number Detour monophonic domination number Upper detour monophonic domination number.
spellingShingle	Monophonic number Domination Number Detour monophonic number Detour monophonic domination number Upper detour monophonic domination number. Khayyoom,M. Mohammed Abdul Characterization of Upper Detour Monophonic Domination Number
description	Abstract This paper introduces the concept of upper detour monophonic domination number of a graph. For a connected graph G with vertex set V (G), a set M ⊆ V (G) is called minimal detour monophonic dominating set, if no proper subset of M is a detour monophonic dominating set. The maximum cardinality among all minimal monophonic dominating sets is called upper detour monophonic domination number and is denoted by γ+ dm (G). For any two positive integers p and q with 2 ≤ p ≤ q there is a connected graph G with γm (G) = γdm (G) = p and γ+ dm (G) = q. For any three positive integers p, q, r with 2 < p < q < r, there is a connected graph G with m(G) = p, γdm (G) = q and γ+ dm (G) = r. Let p and q be two positive integers with 2 < p < q such that γdm (G) = p and γ+ dm (G) = q. Then there is a minimal DMD set whose cardinality lies between p and q. Let p, q and r be any three positive integers with 2 ≤ p ≤ q ≤ r. Then, there exist a connected graph G such that γm (G)= p, γ+ dm (G) = q and \|V (G)\| = r.
author	Khayyoom,M. Mohammed Abdul
author_facet	Khayyoom,M. Mohammed Abdul
author_sort	Khayyoom,M. Mohammed Abdul
title	Characterization of Upper Detour Monophonic Domination Number
title_short	Characterization of Upper Detour Monophonic Domination Number
title_full	Characterization of Upper Detour Monophonic Domination Number
title_fullStr	Characterization of Upper Detour Monophonic Domination Number
title_full_unstemmed	Characterization of Upper Detour Monophonic Domination Number
title_sort	characterization of upper detour monophonic domination number
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2020
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462020000300315
work_keys_str_mv	AT khayyoommmohammedabdul characterizationofupperdetourmonophonicdominationnumber
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Characterization of Upper Detour Monophonic Domination Number

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