【摘要】 如果一个图的全自同构群在其弧集上正则,则称此图为弧正则图.本文刻画素数度的立方自由阶弧正则图,证明任何素数度2倍奇立方自由阶弧正则图都是正规或二部正规Cayley图,且不存在任意素数度4倍奇立方自由阶的弧正则图,推广了一些已知的结果,得到阶为8倍奇平方自由阶素数度弧正则图的分类,并发现新的弧正则图类.此外,基于所得的结果,我们提出一个猜想和有待后续研究的一些问题.更多还原

【Abstract】 A graph is called arc-regular if its full automorphism group acts regularly on its arc set. We characterise arc-regular graphs with prime valency of cube-free order, and prove that such graphs of order twice an odd cube-free integer are normal Cayley graphs or binormal Cayley graphs, and there is no such graph of order four times an odd cube-free integer, which generalises certain previous results in the literature; we also classify arcregular graphs with prime valency of order eight times an odd square-free integer, and found some new arc-regular graphs. Moreover, motivated by the obtained results, a conjecture and some problems are proposed.更多还原