In [3] Cameron et al. classified strongly regular graphs with strongly regular subconstituents. Here we prove a theorem which implies that distance-regular graphs with strongly regular subconstituents are precisely the Taylor graphs and graphs with a1 = 0 and ai ∈ {0, 1} for i = 2, . . . , d .

We prove that, aside from the complete multipartite graphs and graphs of Steiner type, there are only finitely many connected strongly regular graphs with a regular star complement of prescribed degree s ∈ IN . We investigate the possible parameters when s ≤ 5. AMS Classification: 05C50

We consider so-called Fatou-type properties of rational languages and relations. For example, if the rational expression E(X1; : : : ; Xn) over arbitrary languages X1; : : : ;Xn represents a rational language, then each language Xi can be replaced by a rational language Yi such that E(X1; : : : ;Xn) = E(Y1; : : : ; Yn) holds and moreover Xi Yi for i = 1; : : : ; n. Some similar results for rati...

In this paper, we show that the minimum number of vertices whose removal disconnects a connected strongly regular graph into non-singleton components, equals the size of the neighborhood of an edge for many graphs. These include blocks graphs of Steiner 2-designs, many Latin square graphs and strongly regular graphs whose intersection parameters are at most a quarter of their valency.

Bonin et al. (1993) recalled an open problem related to the recurrence relation verified by NSW numbers. The recurrence relation is the following: fn+l = 6f~ f~l , with jq = 1 and j~ = 7, and no combinatorial interpretation seems to be known. In this note, we define a regular language .~ whose number of words having length n is equal to f~+l. Then, by using .La we give a direct combinatorial pr...