5 research outputs found
3-bounded property in a triangle-free distance-regular graph
Let denote a distance-regular graph with classical parameters and . Assume the intersection numbers and
. We show is 3-bounded in the sense of the article
[D-bounded distance-regular graphs, European Journal of Combinatorics(1997)18,
211-229].Comment: 13 page
A characterization of the Hamming graph by strongly closed subgraphs
AbstractThe Hamming graph H(d,q) satisfies the following conditions: (i)For any pair (u,v) of vertices there exists a strongly closed subgraph containing them whose diameter is the distance between u and v. In particular, any strongly closed subgraph is distance-regular.(ii)For any pair (x,y) of vertices at distance d−1 the subgraph induced by the neighbors of y at distance d from x is a clique of size a1+1.In this paper we prove that a distance-regular graph which satisfies these conditions is a Hamming graph
Distance-regular graphs
This is a survey of distance-regular graphs. We present an introduction to
distance-regular graphs for the reader who is unfamiliar with the subject, and
then give an overview of some developments in the area of distance-regular
graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A.,
Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.Comment: 156 page