Abstract
Alspach et al. (J. Austral. Math. Soc. 56(3) (1994) 391–402) constructed an infinite family of tetravalent graphs M(a; m, n) and proved that if \(n\ge 9\) be odd and \(a^3\equiv 1 (\mathrm{mod}~n)\), then M(a; 3, n) is half-arc-transitive. In this paper, we show that if \(a^3\equiv 1 (\mathrm{mod}~n)\) , then M(a; 3, n) is an infinite family of tetravalent half-arc-transitive Cayley graphs for all integers n except 7 and 14.
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Acknowledgements
The first author is supported by the Ph.D. Fellowship of CSIR (File No. 08/155(0086)/2020-EMR-I), Government of India. The second author acknowledges the funding of DST-SERB-SRG Sanction No. SRG/2019/000475, Govt. of India.
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Communicating Editor: Sukanta Pati
Appendix
Appendix
Appendix A: Sage Code for \(\Gamma (n,a)\) for \(n=7, a=2\):
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Biswas, S., Das, A. A family of tetravalent half-arc-transitive graphs. Proc Math Sci 131, 28 (2021). https://doi.org/10.1007/s12044-021-00625-8
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DOI: https://doi.org/10.1007/s12044-021-00625-8