Czechoslovak Mathematical Journal, Vol. 69, No. 2, pp. 391-401, 2019
Tetravalent half-arc-transitive graphs of order $p^2q^2$
Hailin Liu, Bengong Lou, Bo Ling
Received July 15, 2017. Published online February 4, 2019.
Abstract: We classify tetravalent $G$-half-arc-transitive graphs $\Gamma$ of order $p^2q^2$, where $G\leq\mathop{\textsf{Aut}}\Gamma$ and $p$, $q$ are distinct odd primes. This result involves a subclass of tetravalent half-arc-transitive graphs of cube-free order.
Keywords: half-arc-transitive graph; normal Cayley graph; cube-free order
Affiliations: Hailin Liu, School of Science, Jiangxi University of Science and Technology, No. 86, Hongqi Ave, Ganzhou, Jiangxi 341000, P. R. China, e-mail: hailinliuqp@163.com; Hailin Liu, Bengong Lou (corresponding author), School of Mathematics and Statistics, Yunnan University, No. 2, Cuihubei Rd, Kunming 650091 P. R. China, e-mail: bengong188@163.com; Bo Ling, School of Mathematics and Computer Science, Yunnan Minzu University, No. 2929, Yuehua Ave, Kunming 650504, P. R. China, e-mail: bolinggxu@163.com