Hamiltonian Strongly Regular Graphs

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.Distance-regular graphs;Hamilton cycles JEL-code

The Gewirtz graph: An exercise in the theory of graph spectra

Graphs;mathematics

The Integral Trees with Spectral Radius 3

There are eleven integral trees with largest eigenvalue 3.Integral graphs;graph spectra;trees

Eigenvalues and Perfect Matchings

AMS classification: 05C50, 05C70, 05E30.graph;perfect matching;Laplacian matrix;eigenvalues.

Two distance-regular graphs

We construct two families of distance-regular graphs, namely the subgraph of the dual polar graph of type B_3(q) induced on the vertices far from a fixed point, and the subgraph of the dual polar graph of type D_4(q) induced on the vertices far from a fixed edge. The latter is the extended bipartite double of the former