一类具有唯一定长路的有向图的自同构群

The Automorphism Groups for a Kind of Directed Graphs with Unique Paths of Fixed Length

Ｌａｍ和Ｖａｎ Ｌｉｎｔ 在推广友谊定理时构造了一类具有唯一定长路的有向图（这里 用Ｄ（ｃ，ｋ）表示），并证明了Ｄ（ｃ，ｋ）的自同构群包含一个２（ｃ＋１）阶二面体群。 木文利用Ｄ（ｃ．ｋ）的邻接矩阵的性质证明这个二面体群就是Ｄ（ｃ，ｋ）的全自同构群， 从而解决了 Ｌａｍ和 Ｖａｎ Ｌｉｎｔ作中遗留的问题。

Lam and Van Lint, in their generalization of the Friendship Theorem, construct a kind of directed graphs with unique paths of fixed length, here denoted by D(c, k), and have proved that the automorphism group for D(c,k) contains a dihedral group of order 2(c+1). The author has proved that the dihedral group is just the full automorphism group for D(c, k), using the properties of the adjacent matrix of D(c, k). Hence, a problem left over in Lam and Van Lint's work has been solved.