2010 Mathematics Subject Classification: 05E30, 05C50;

We give a sufficient condition for a distance-regular graph to be Hamiltonian. In particular, the Petersen graph is the only connected non-Hamiltonian strongly regular graph on fewer than 99 vertices.

In [E.R. van Dam and W.H. Haemers, Which graphs are determined by their spectrum?, Linear Algebra Appl. 373 (2003), 241-272] we gave a survey of answers to the question of which graphs are determined by the spectrum of some matrix associated to the graph. In particular, the usual adjacency...

We show that the Hamming graph H(3; q) with diameter three is uniquely determined by its spectrum for q ¸ 36. Moreover, we show that for given integer D ¸ 2, any graph cospectral with the Hamming graph H(D; q) is locally the disjoint union of D copies of the complete graph of size q ¡ 1, for q...

AMS classifications: 05E30; 05B20

AMS classification: 05E30