Tetravalent edge-transitive Cayley graphs of Frobenius groups

Abstract

In this paper, we give a characterisation for a class of edge-transitive Cayley graphs and provide a method for constructing edge-transitive graphs of valency 4 with arbitrarily large vertex stabiliser. In particular, in the last section, we obtain certain extensions of the results of Li et al. (Tetravalent edge-transitive Cayley graphs with odd number of vertices, J Comb Theory Ser B 96:164–181, 2006) on half-transitive graphs.

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Correspondence to Yin Liu.

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This work was supported by Natural Science Foundation of China (No. 12061083); Educational Department Fund of Yunnan (No. 2019J0026); NSF of Yunnan Province (No. 2017FD071); Natural Science Foundation of China (Nos. 11671324; 11971391); Fundamental Research Funds for the Central Universities (Nos. XDJK2019C116; XDJK2019B030) and Teaching Reform Project of Southwest University (No. 2018JY061).

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Wang, L., Liu, Y. & Yan, Y. Tetravalent edge-transitive Cayley graphs of Frobenius groups. J Algebr Comb (2021). https://doi.org/10.1007/s10801-020-01005-7

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Keywords

  • Frobenius group
  • Edge-transitive graph
  • Coset graph
  • Cayley graph

Mathematics Subject Classification

  • 05C25
  • 05E18