The matching polynomial of a distance-regular graph
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 ma...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200000740 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |