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
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.
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