A paradigmatic approach to investigate restricted hyper totient graphs

Nowadays, the problem of finding families of graphs for which one may ensure the existence of a vertex-labeling and/or an edge-labeling based on a certain class of integers, constitutes a challenge for researchers in both number and graph theory. In this paper, we focus on those vertexlabelings whos...

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Detalhes bibliográficos
Autores: Ali, Shahbaz, Mahmmod, Muhammad Khalid, Falcón Ganfornina, Raúl Manuel
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/111711
Acesso em linha:https://hdl.handle.net/11441/111711
https://doi.org/10.3934/math.2021223
Access Level:acceso abierto
Palavra-chave:Graph labeling
Hyper totient number
Hyper totient graph
Restricted hyper totient graph
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spelling A paradigmatic approach to investigate restricted hyper totient graphsAli, ShahbazMahmmod, Muhammad KhalidFalcón Ganfornina, Raúl ManuelGraph labelingHyper totient numberHyper totient graphRestricted hyper totient graphNowadays, the problem of finding families of graphs for which one may ensure the existence of a vertex-labeling and/or an edge-labeling based on a certain class of integers, constitutes a challenge for researchers in both number and graph theory. In this paper, we focus on those vertexlabelings whose induced multiplicative edge-labeling assigns hyper totient numbers to the edges of the graph. In this way, we introduce and characterize the notions of hyper totient graph and restricted hyper totient graph. In particular, we prove that every finite graph is a hyper totient graph and we determine under which assumptions the following families of graphs constitute restricted hyper totient graphs: complete graphs, star graphs, complete bipartite graphs, wheel graphs, cycles, paths, fan graphs and friendship graphs.Junta de Andalucía FQM-016AIMS PressMatemática Aplicada IJunta de Andalucía2021info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/111711https://doi.org/10.3934/math.2021223reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésAIMS Mathematics, 6 (4), 3761-3771.FQM-016https://www.aimspress.com/article/doi/10.3934/math.2021223info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1117112026-06-17T12:51:07Z
dc.title.none.fl_str_mv A paradigmatic approach to investigate restricted hyper totient graphs
title A paradigmatic approach to investigate restricted hyper totient graphs
spellingShingle A paradigmatic approach to investigate restricted hyper totient graphs
Ali, Shahbaz
Graph labeling
Hyper totient number
Hyper totient graph
Restricted hyper totient graph
title_short A paradigmatic approach to investigate restricted hyper totient graphs
title_full A paradigmatic approach to investigate restricted hyper totient graphs
title_fullStr A paradigmatic approach to investigate restricted hyper totient graphs
title_full_unstemmed A paradigmatic approach to investigate restricted hyper totient graphs
title_sort A paradigmatic approach to investigate restricted hyper totient graphs
dc.creator.none.fl_str_mv Ali, Shahbaz
Mahmmod, Muhammad Khalid
Falcón Ganfornina, Raúl Manuel
author Ali, Shahbaz
author_facet Ali, Shahbaz
Mahmmod, Muhammad Khalid
Falcón Ganfornina, Raúl Manuel
author_role author
author2 Mahmmod, Muhammad Khalid
Falcón Ganfornina, Raúl Manuel
author2_role author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
Junta de Andalucía
dc.subject.none.fl_str_mv Graph labeling
Hyper totient number
Hyper totient graph
Restricted hyper totient graph
topic Graph labeling
Hyper totient number
Hyper totient graph
Restricted hyper totient graph
description Nowadays, the problem of finding families of graphs for which one may ensure the existence of a vertex-labeling and/or an edge-labeling based on a certain class of integers, constitutes a challenge for researchers in both number and graph theory. In this paper, we focus on those vertexlabelings whose induced multiplicative edge-labeling assigns hyper totient numbers to the edges of the graph. In this way, we introduce and characterize the notions of hyper totient graph and restricted hyper totient graph. In particular, we prove that every finite graph is a hyper totient graph and we determine under which assumptions the following families of graphs constitute restricted hyper totient graphs: complete graphs, star graphs, complete bipartite graphs, wheel graphs, cycles, paths, fan graphs and friendship graphs.
publishDate 2021
dc.date.none.fl_str_mv 2021
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/111711
https://doi.org/10.3934/math.2021223
url https://hdl.handle.net/11441/111711
https://doi.org/10.3934/math.2021223
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv AIMS Mathematics, 6 (4), 3761-3771.
FQM-016
https://www.aimspress.com/article/doi/10.3934/math.2021223
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv AIMS Press
publisher.none.fl_str_mv AIMS Press
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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