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

Distance-Regular Graphs with an Eigenvalue of Multiplicity Four

AbstractLet G be a distance-regular graph. If G has an eigenvalue θ of multiplicity m (≥ 2), then G has a natural representation in Rm. By studying the geometric properties of the image configuration in Rm, we can obtain considerable information about the graph-theoretic properties of G itself. This sets the basis for classifying distance-regular graphs by their eigenvalue multiplicities. It is known that the distance-regular graphs with an eigenvalue of multiplicity three are exactly the five Platonic solids plus all complete 4-partite regular graphs. In this paper we classify the distance-regular graphs with an eigenvalue of multiplicity four