Krein parameters and antipodal tight graphs with diameter 3 and 4

AbstractWe determine which Krein parameters of nonbipartite antipodal distance-regular graphs of diameter 3 and 4 can vanish, and give combinatorial interpretations of their vanishing. We also study tight distance-regular graphs of diameter 3 and 4. In the case of diameter 3, tight graphs are precisely the Taylor graphs. In the case of antipodal distance-regular graphs of diameter 4, tight graphs are precisely the graphs for which the Krein parameter q114 vanishes

On distance regular graphs with b2=1 and antipodal covers

This thesis is an exposition of the paper entitled On Distance Regular Graphs with b2 = 1 and Antipodal Covers by Makoto Araya, Akira Hiraki, and Alexander Jurisic.Let T be a Distance Regular Graph of valency k2. It is shown that if b2 = 1, the T is antipodal and one of the following holds:(1) T is the dodecahedron(2) d = 4 and T is antipodal double cover for a Strongly Regular Graph with parameters (k, a1, c2) = (n2 + 1, 0, 2) for an integer n not divisible by four.(3) d = 3 and T is an antipodal cover of a complete 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