科研之友
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摘要
A digraph is k-transitive, if for any a path x(0)x(1) ... x(k) of length k, x(0) dominates x(k). A digraph is a strong k-transitive digraph, if it is k-transitive and it is strongly connected. Cesar Hernandez-Cruz proposed the following conjecture: Let k - 1 be a prime and D be a strong k-transitive digraph. If vertical bar V (D) vertical bar >= k + 1, D contains an n-cycle, with n >= k and (n, k - 1) = 1, and D is not a symmetrical (k + 1)-cycle, then D is a complete digraph. In this paper, we shall prove that the conjecture is true.
- 出版日期2012-4-28
- 单位山西大学
