Talk:Distance-regular graph

The sentence "... such that for any two vertices v and w at distance i, the number of vertices adjacent to w and the number of vertices at distance j from v is the same." is unclear -- are i and j chosen a-priori, or does it mean that, given v and w (with a particular distance from one-another), we can find some j for which the number of vertices at distance j from v is the same as the number of vertices adjacent to w? The sentence could use some re-wording if so, to make clear that there is perhaps only one value among many of j for which this equality will be satisfied. Furthermore, if this is a correct interpretation, then there is really no need to refer to i at all, since we can simply state that v and w have a fixed distance between them. 24.11.104.3 (talk) 18:29, 19 January 2013 (UTC)[reply]

The "valency" of a distance regular graph is referred to but not defined. — Preceding unsigned comment added by 199.249.110.156 (talk) 00:00, 16 August 2018 (UTC)[reply]

Now linked to Degree (graph theory) where it is defined. —David Eppstein (talk) 00:27, 16 August 2018 (UTC)[reply]