this is the case.As a consequence we find (among others) that the following distance-regular graphs are uniquely determined … by their spectrum: The collinearity graphs of the generalized octagons of order (2; 1), (3; 1) and (4; 1), the Biggs …-Smith graph, the M22 graph, and the coset graphs of the doubly truncated binary Golay code and the extended ternary Golay code. …

We give several old and some new applications of eigenvalue interlacing to matrices associated to graphs. Bounds are … obtained for characteristic numbers of graphs, such as the size of a maximal (co)clique, the chromatic number, the diameter and … inequalities and regularity results concerning the structure of graphs and block designs. …

We characterize the distance-regular graphs with diameter three by giving an expression for the number of vertices at …

given and characterized. A list of feasible parameter sets for graphs with at most 40 vertices is generated. …