Cayley numbers with arbitrarily many distinct prime factors

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• 作者：Ted Dobson^a ; ^b ; ^{dobson@math.msstate.edu} ; Pablo Spiga^c ; ^{pablo.spiga@unimib.it}
• 关键词：Vertex-transitive ; Cayley graph ; Cayley number ; Semiregular
• 刊名：Journal of Combinatorial Theory, Series B
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：122
• 期：Complete
• 页码：301-310
• 全文大小：306 K
• 卷排序：122

文摘

A positive integer n is a Cayley number if every vertex-transitive graph of order n is a Cayley graph. In 1983, Dragan Marušič posed the problem of determining the Cayley numbers. In this paper we give an infinite set S of primes such that every finite product of distinct elements from S is a Cayley number. This answers a 1996 outstanding question of Brendan McKay and Cheryl Praeger, which they “believe to be the key unresolved question” on Cayley numbers. We also show that, for every finite product n of distinct elements from S, every transitive group of degree n contains a semiregular element.