International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 2, Pages 89-97
doi:10.1155/S0161171200000740
The matching polynomial of a distance-regular graph
Robert A. Beezer1
and E.J. Farrell2
1Department of Mathematics and Computer Science, University of Puget Sound, Tacoma, Washington 98416, USA
2Department of Mathematics, University of the West Indies, St. Augustine, Trinidad and Tobago
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.