International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 2, Pages 89-97
The matching polynomial of a distance-regular graph
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
Received 15 August 1997
Copyright © 2000 Robert A. Beezer and E. J. Farrell. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A distance-regular graph of diameter has 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.