Title

The matching polynomial of a distance-regular graph

Document Type

Article

Publication Date

2000

Publication Title

International Journal of Mathematics and Mathematical Sciences

Department

Mathematics and Computer Science

Abstract

A distance-regular graph of diameter d has 2d intersection numbers that determine many properties of graph (e.g., its spectrum). We show that the first six coefficients of the matching polynomial of a distance-regular graph can also be determined from its intersection array, and that this is the maximum number of coefficients so determined. Also, the converse is true for distance-regular graphs of small diameter—that is, the intersection array of a distance-regular graph of diameter 3 or less can be determined from the matching polynomial of the graph.

ISSN

0161-1712