1. A new class of graceful graphs: k-enriched fan graphs and their characterisations
| Title | A new class of graceful graphs: k-enriched fan graphs and their characterisations |
|---|---|
| Author info | Miroslav Haviar, Samuel Kurtulík |
| Author | Haviar Miroslav 1965- (50%) UMBFP10 - Katedra matematiky |
| Co-authors | Kurtulík Samuel (50%) |
| Source document | Cubo : a mathematical journal. Vol. 23, č. 2 (2021), pp. 313-331. - Temuco : Department of mathematics and statistics of the Universidad de La Frontera, 2021 |
| Keywords | grafy - charts - graphs graciózne ohodnotenie grafov - graceful labelling of graphs grafové šachovnice - graph chessboards postupnosť |
| Form. Descr. | články - journal articles |
| Language | English |
| Country | Chile |
| Annotation | The 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 ≥ 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. |
| URL | Link na zdrojový dokument Link na plný text |
| Public work category | ADM |
| No. of Archival Copy | 50548 |
| Catal.org. | BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici |
| Database | xpca - PUBLIKAČNÁ ČINNOSŤ |
| References | PERIODIKÁ-Súborný záznam periodika |