The matching polynomial of a distance-regular graph
International Journal of Mathematics and Mathematical Sciences
Mathematics and Computer Science
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.
Beezer, Robert A, and E J. Farrell. "The Matching Polynomial of a Distance-Regular Graph." International Journal of Mathematics and Mathematical Sciences. 23.2 (2000): 89-97. Print.