Doubly regular asymmetric digraphs

Noboru Ito
1988 Discrete Mathematics  
Remark. The case where the equality holds in Proposition 1 corresponds to the case of' Hadamard tournaments. For this see [ 1, 4 and 61. Proposition 2. D is strongly connected. Proof. Let a be any vertex and C(a) the set of vertices to which there exist (directed) paths from a. By the definition of a DRAD it is easy to see that (i) there exists a vertex a such that C(u) = V and (ii) V = {a E V; C(a) = V}. Ei Proposition 3. Let a be any vertex, N:(u) the set of vertices whose distance from a
more » ... ls two and N;(u) the set of vertices whose distance to a equals two. Then IN:(a)1 und IN;(u)1 are not fess than (n2/2A) + (in) -(3W3), where n = k -A.
doi:10.1016/0012-365x(88)90208-7 fatcat:sh2mc77g5bg6raomxxlpc5bn7y