The matching polynomial of a distance-regular graph (Q1975936)

It is well known that a distance-regular graph of diameter \(d\) has \(2d\) intersection numbers. It is shown in this paper 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. It is also shown that the converse is true for distance-regular graphs of small diameter, i.e. the intersection array of a distance-regular graph of diameter 3 or less can be determined from the matching polynomial of the graph.