A survey and a new class of graceful unicylic graphs
| Autor: | Max Pambe Biatch’, Jay S. Bagga, S. Arumugam |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | AKCE International Journal of Graphs and Combinatorics, Vol 17, Iss 2, Pp 673-678 (2020) |
| Druh dokumentu: | article |
| ISSN: | 0972-8600 2543-3474 09728600 |
| DOI: | 10.1080/09728600.2020.1832853 |
| Popis: | A graph G admits a graceful labeling if there is a one-to-one map f from the set of vertices of G to such that when an edge xy is assigned the label the resulting set of edge labels is When such a labeling exists, G is called graceful. Rosa showed that a cycle Cn () is graceful if and only if n is congruent to 0 or 3 modulo 4. Truszczyński conjectured that unicyclic graphs, except the cycles in Rosa’s result are graceful. Several classes of unicyclic graphs are known to be graceful. In this article, we present a survey of results related to Truszczyński’s conjecture. We also present a new class of graceful unicyclic graphs. |
| Databáze: | Directory of Open Access Journals |
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