| Autor: |
Ana Granados, Domingo Pestana, Ana Portilla, José M. Rodríguez |
| Jazyk: |
angličtina |
| Rok vydání: |
2017 |
| Předmět: |
|
| Zdroj: |
Symmetry, Vol 9, Iss 8, p 131 (2017) |
| Druh dokumentu: |
article |
| ISSN: |
2073-8994 |
| DOI: |
10.3390/sym9080131 |
| Popis: |
Since the characterization of Gromov hyperbolic graphs seems a too ambitious task, there are many papers studying the hyperbolicity of several classes of graphs. In this paper, it is proven that every Mycielskian graph G M is hyperbolic and that δ ( G M ) is comparable to diam ( G M ) . Furthermore, we study the extremal problems of finding the smallest and largest hyperbolicity constants of such graphs; in fact, it is shown that 5 / 4 ≤ δ ( G M ) ≤ 5 / 2 . Graphs G whose Mycielskian have hyperbolicity constant 5 / 4 or 5 / 2 are characterized. The hyperbolicity constants of the Mycielskian of path, cycle, complete and complete bipartite graphs are calculated explicitly. Finally, information on δ ( G ) just in terms of δ ( G M ) is obtained. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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