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
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
is hyperbolic and that
is comparable to
. Furthermore, we study the extremal problems of finding the smallest and largest hyperbolicity constants of such graphs; in fact, it is shown that
. Graphs G
whose Mycielskian have hyperbolicity constant
are characterized. The hyperbolicity constants of the Mycielskian of path, cycle, complete and complete bipartite graphs are calculated explicitly. Finally, information on
just in terms of
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).
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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.
Granados A, Pestana D, Portilla A, Rodríguez JM. Gromov Hyperbolicity in Mycielskian Graphs. Symmetry. 2017; 9(8):131.
Granados, Ana; Pestana, Domingo; Portilla, Ana; Rodríguez, José M. 2017. "Gromov Hyperbolicity in Mycielskian Graphs." Symmetry 9, no. 8: 131.
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