The forcing total monophonic number of a graph

Abstract For a connected graph G = (V, E) of order at least two, a subset T of a minimum total monophonic set S of G is a forcing total monophonic subset for S if S is the unique minimum total monophonic set containing T . A forcing total monophonic subset for S of minimum cardinality is a minimum f...

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Autores principales:	Santhakumaran,A. P., Titus,P., Ganesamoorthy,K., Murugan,M.
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2021
Materias:	Total monophonic set Total monophonic number Forcing total monophonic subset Forcing total monophonic number
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000200561
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spelling	oai:scielo:S0716-091720210002005612021-04-03The forcing total monophonic number of a graphSanthakumaran,A. P.Titus,P.Ganesamoorthy,K.Murugan,M. Total monophonic set Total monophonic number Forcing total monophonic subset Forcing total monophonic number Abstract For a connected graph G = (V, E) of order at least two, a subset T of a minimum total monophonic set S of G is a forcing total monophonic subset for S if S is the unique minimum total monophonic set containing T . A forcing total monophonic subset for S of minimum cardinality is a minimum forcing total monophonic subset of S. The forcing total monophonic number f tm (S) in G is the cardinality of a minimum forcing total monophonic subset of S. The forcing total monophonic number of G is f tm (G) = min{f tm (S)}, where the minimum is taken over all minimum total monophonic sets S in G. We determine bounds for it and find the forcing total monophonic number of certain classes of graphs. It is shown that for every pair a, b of positive integers with 0 ≤ a < b and b ≥ a+4, there exists a connected graph G such that f tm (G) = a and m t (G) = b.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.40 n.2 20212021-04-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000200561en10.22199/issn.0717-6279-2021-02-0031
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Total monophonic set Total monophonic number Forcing total monophonic subset Forcing total monophonic number
spellingShingle	Total monophonic set Total monophonic number Forcing total monophonic subset Forcing total monophonic number Santhakumaran,A. P. Titus,P. Ganesamoorthy,K. Murugan,M. The forcing total monophonic number of a graph
description	Abstract For a connected graph G = (V, E) of order at least two, a subset T of a minimum total monophonic set S of G is a forcing total monophonic subset for S if S is the unique minimum total monophonic set containing T . A forcing total monophonic subset for S of minimum cardinality is a minimum forcing total monophonic subset of S. The forcing total monophonic number f tm (S) in G is the cardinality of a minimum forcing total monophonic subset of S. The forcing total monophonic number of G is f tm (G) = min{f tm (S)}, where the minimum is taken over all minimum total monophonic sets S in G. We determine bounds for it and find the forcing total monophonic number of certain classes of graphs. It is shown that for every pair a, b of positive integers with 0 ≤ a < b and b ≥ a+4, there exists a connected graph G such that f tm (G) = a and m t (G) = b.
author	Santhakumaran,A. P. Titus,P. Ganesamoorthy,K. Murugan,M.
author_facet	Santhakumaran,A. P. Titus,P. Ganesamoorthy,K. Murugan,M.
author_sort	Santhakumaran,A. P.
title	The forcing total monophonic number of a graph
title_short	The forcing total monophonic number of a graph
title_full	The forcing total monophonic number of a graph
title_fullStr	The forcing total monophonic number of a graph
title_full_unstemmed	The forcing total monophonic number of a graph
title_sort	forcing total monophonic number of a graph
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2021
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000200561
work_keys_str_mv	AT santhakumaranap theforcingtotalmonophonicnumberofagraph AT titusp theforcingtotalmonophonicnumberofagraph AT ganesamoorthyk theforcingtotalmonophonicnumberofagraph AT muruganm theforcingtotalmonophonicnumberofagraph AT santhakumaranap forcingtotalmonophonicnumberofagraph AT titusp forcingtotalmonophonicnumberofagraph AT ganesamoorthyk forcingtotalmonophonicnumberofagraph AT muruganm forcingtotalmonophonicnumberofagraph
_version_	1718439900917792768

The forcing total monophonic number of a graph

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