Cayley图的泛因子性质(英文)

On the Panfactorical Property of Cayley Graphs

英文关键词:panfactorial  Cayley graph  finite group  factorization.

中文摘要:

      一个κ-正则图若满足对任意正整数s,1≤s≤κ,均存在一个s-因子或一个2[s/2]因子,则称其有泛因子或偶泛因子性质.本文证明了每个奇度Cayley图是泛因子的,每个偶度Carley图是偶泛因子的.同时证明了二面体群上的每个Cayley图均是泛因子的.

英文摘要:

      A k-regular graph is called panfactorical, or even panfactorical respectively,if for every integer s, 1 ≤ s ≤ k,there exists an s-factor, or 2[s/2]-factor, in this graph.A criterion for checking an r-regular graph to be panfactorical or even panfactorical isestablished. It is proved that every Cayley graph of odd degree is panfactorical and everyCayley graph of even degree is even panfactorical by using this criterion. For a dihedralgroup, we prove that every connected Cayley graph on this group is panfactorial.