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Open AccessFeature PaperArticle

Gromov Hyperbolicity in Mycielskian Graphs

Department of Mathematics and Computer Science, Saint Louis University, Avenida del Valle 34, 28003 Madrid, Spain
Department of Mathematics, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain
Author to whom correspondence should be addressed.
Academic Editor: Angel Garrido
Symmetry 2017, 9(8), 131;
Received: 21 June 2017 / Revised: 14 July 2017 / Accepted: 21 July 2017 / Published: 27 July 2017
(This article belongs to the Special Issue Graph Theory)
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. View Full-Text
Keywords: extremal problems on graphs; Mycielskian graphs; geodesics; Gromov hyperbolicity extremal problems on graphs; Mycielskian graphs; geodesics; Gromov hyperbolicity
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MDPI and ACS Style

Granados, A.; Pestana, D.; Portilla, A.; Rodríguez, J.M. Gromov Hyperbolicity in Mycielskian Graphs. Symmetry 2017, 9, 131.

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