Classifying pentavalent symmetric graphs of order 12pq

Abstract

A graph is said to be symmetric if its automorphism group is transitive on its arcs. Guo et al. (Pentavalent symmetric graphs of order 12p, Electron. J. Combin. 18 (2011), no. 1, #P233, DOI: https://doi.org/10.37236/720) and Ling (Classifying pentavalent symmetric graphs of order 24p, Bull. Iranian Math. Soc. 43 (2017), no. 6, 1855–1866) Li and Ling (Symmetric graphs and interconnection networks, Future Gener. Comput. Syst. 83 (2018), no. 1, 461–467, DOI: https://doi.org/10.1016/j.future.2017.05.016) determined all pentavalent symmetric graphs of order 12p12p, 24p24p, and 36p36p. In this article, we shall generalize these results by determining all connected pentavalent symmetric graphs of order 12pq12pq, where p>qp\gt q are distinct primes.

Keywords

• symmetric graph
• normal quotient
• automorphism group
• 05c25
• 05e18