A Lower Bound for the Spectral Radius of Graphs with Fixed Diameter

AMS classifications: 05C50, 05E99;graphs;spectral radius;diameter;bound;degree/diameter

Asymptotic Results on the Spectral Radius and the Diameter of Graphs

2000 Mathematics Subject Classification: 05C50, 05E99;graphs;spectral radius;diameter;limit points;quipus

Spectral Characterization of the Hamming Graphs

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 large enough.Hamming graphs;distance-regular graphs;eigenvalues of graphs

Cospectral Graphs and the Generalized Adjacency Matrix

AMS classifications: 05C50; 05E99;cospectral graphs;generalized spectrum;generalized adjacency matrix