International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2000 / Article

Open Access

Volume 23 |Article ID 651078 | https://doi.org/10.1155/S0161171200000740

Robert A. Beezer, E. J. Farrell, "The matching polynomial of a distance-regular graph", International Journal of Mathematics and Mathematical Sciences, vol. 23, Article ID 651078, 9 pages, 2000. https://doi.org/10.1155/S0161171200000740

The matching polynomial of a distance-regular graph

Received15 Aug 1997

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.

Copyright © 2000 Hindawi Publishing Corporation. 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.


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