Next Article in Journal
Distribution of Antennal Olfactory and Non-Olfactory Sensilla in Different Species of Bees
Next Article in Special Issue
Generalized Chordality, Vertex Separators and Hyperbolicity on Graphs
Previous Article in Journal / Special Issue
The Simultaneous Local Metric Dimension of Graph Families
Article Menu
Issue 8 (August) cover image

Export Article

Open AccessFeature PaperArticle
Symmetry 2017, 9(8), 131;

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
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)
Full-Text   |   PDF [850 KB, uploaded 28 July 2017]   |  


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

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top