The present article is designed to be a contribution to the chapter 'Combinatorial Matrix Theory and Graphs' of the Handbook of Linear Algebra, to be published by CRC Press. The format of the handbook is to give just definitions, theorems, and examples; no proofs. In the five sections given...

We give sufficient conditions for existence of a perfect matching in a graph in terms of the eigenvalues of the Laplacian matrix. We also show that a distance-regular graph of degree k is k-edge-connected