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dc.creatorHaviar, M.
dc.creatorKurtulík, S.
dc.date2021-08-01
dc.identifierhttps://revistas.ufro.cl/ojs/index.php/cubo/article/view/2729
dc.identifier10.4067/S0719-06462021000200313
dc.descriptionThe Graceful Tree Conjecture stated by Rosa in the mid 1960s says that every tree can be gracefully labelled. It is one of the best known open problems in Graph Theory. The conjecture has caused a great interest in the study of gracefulness of simple graphs and has led to many new contributions to the list of graceful graphs. However, it has to be acknowledged that not much is known about the structure of graceful graphs after 55 years. Our paper adds an infinite family of classes of graceful graphs to the list of known simple graceful graphs. We introduce classes of \(k\)-enriched fan graphs \(kF_n\) for all integers \(k, n\ge 2\) and we prove that these graphs are graceful. Moreover, we provide characterizations of the \(k\)-enriched fan graphs \(kF_n\) among all simple graphs via Sheppard's labelling sequences introduced in the 1970s, as well as via labelling relations and graph chessboards. These last approaches are new tools for the study of graceful graphs introduced by Haviar and Ivaška in 2015. The labelling relations are closely related to Sheppard's labelling sequences while the graph chessboards provide a nice visualization of graceful labellings. We close our paper with an open problem concerning another infinite family of extended fan graphs.en-US
dc.formatapplication/pdf
dc.languageeng
dc.publisherUniversidad de La Frontera. Temuco, Chile.en-US
dc.relationhttps://revistas.ufro.cl/ojs/index.php/cubo/article/view/2729/2094
dc.rightsCopyright (c) 2021 M. Haviar et al.en-US
dc.rightshttps://creativecommons.org/licenses/by-nc/4.0/en-US
dc.sourceCUBO, A Mathematical Journal; Vol. 23 No. 2 (2021); 313–331en-US
dc.sourceCUBO, A Mathematical Journal; Vol. 23 Núm. 2 (2021); 313–331es-ES
dc.source0719-0646
dc.source0716-7776
dc.subjectgraphen-US
dc.subjectgraceful labellingen-US
dc.subjectgraph chessboarden-US
dc.subjectlabelling sequenceen-US
dc.subjectlabelling relationen-US
dc.titleA new class of graceful graphs: \(k\)-enriched fan graphs and their characterisationsen-US
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion


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