When is Cartesian product a Cayley graph?

EUROCOMB’23

Edward Dobson Ademir Hujdurović Wilfried Imrich Ronald Ortner

https://doi.org/10.5817/CZ.MUNI.EUROCOMB23-050

PDF
Abstract
A graph is said to be a Cayley graph if its automorphism group admits a regular subgroup. Automorphisms of the Cartesian product of graphs are well understood, and it is known that Cartesian product of Cayley graphs is a Cayley graph. It is natural to ask the reverse question, namely whether all the factors of Cartesian product that is a Cayley graph have to be Cayley graphs. The main purpose of this paper is to initiate the study of this question.

Pages:
362–367
References

Ted Dobson, Aleksander Malnic, and Dragan Marušic, Symmetry in graphs, Cambridge Studies in Advanced Mathematics, vol. 198, Cambridge University Press, Cambridge, 2022.

Richard Hammack, Wilfried Imrich, and Sandi Klavžar, Handbook of product graphs, second ed., Discrete Mathematics and its Applications (Boca Raton), CRC Press, Boca Raton, FL, 2011.
https://doi.org/10.1201/b10959

Ademir Hujdurovic, Klavdija Kutnar, and Dragan Marušic, On normality of n-Cayley graphs, Appl. Math. Comput. 332 (2018), 469-476.
https://doi.org/10.1016/j.amc.2018.03.054

Donald Passman, Permutation groups, W. A. Benjamin, Inc., New York-Amsterdam, 1968.

Gert Sabidussi, Vertex-transitive graphs, Monatsh. Math. 68 (1964), 426-438.
https://doi.org/10.1007/BF01304186

Metrics

0

Views

0

PDF views

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Copyright © 2023 Edward Dobson, Ademir Hujdurović, Wilfried Imrich, Ronald Ortner

PDF