We show that the large Cartesian powers of any graph have log-concave valencies with respect to a ffxed vertex. We show that the series of valencies of distance regular graphs is log-concave, thus improving on a result of (Taylor, Levingston, 1978). Consequences for strongly regular graphs, two-weight codes, and completely regular codes are derived. By P-Q duality of association schemes the series of multiplicities of Q-polynomial association schemes is shown, under some assumption, to be log-concave.

翻译：我们证明了任意图的大笛卡尔幂相对于固定顶点具有对数凹的度序列。我们证明了距离正则图的度序列具有对数凹性，从而改进了(Taylor, Levingston, 1978)的结果。由此推导出强正则图、双权码和完全正则码的相关性质。通过结合方案的P-Q对偶性，我们证明了在特定条件下，Q-多项式结合方案的重数序列具有对数凹性。