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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2000-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200000740 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832567058444845056 |
|---|---|
| author | Robert A. Beezer E. J. Farrell |
| author_facet | Robert A. Beezer E. J. Farrell |
| author_sort | Robert A. Beezer |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c1ff254edc0a4638a2f10b8ffc16202a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c1ff254edc0a4638a2f10b8ffc16202a2025-02-03T01:02:30ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-01232899710.1155/S0161171200000740The matching polynomial of a distance-regular graphRobert A. Beezer0E. J. Farrell1Department of Mathematics and Computer Science, University of Puget Sound, Tacoma, Washington 98416, USADepartment of Mathematics, University of the West Indies, St. Augustine, Trinidad and TobagoA 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.http://dx.doi.org/10.1155/S0161171200000740Matching polynomialdistance-regular graph. |
| spellingShingle | Robert A. Beezer E. J. Farrell The matching polynomial of a distance-regular graph International Journal of Mathematics and Mathematical Sciences Matching polynomial distance-regular graph. |
| title | The matching polynomial of a distance-regular graph |
| title_full | The matching polynomial of a distance-regular graph |
| title_fullStr | The matching polynomial of a distance-regular graph |
| title_full_unstemmed | The matching polynomial of a distance-regular graph |
| title_short | The matching polynomial of a distance-regular graph |
| title_sort | matching polynomial of a distance regular graph |
| topic | Matching polynomial distance-regular graph. |
| url | http://dx.doi.org/10.1155/S0161171200000740 |
| work_keys_str_mv | AT robertabeezer thematchingpolynomialofadistanceregulargraph AT ejfarrell thematchingpolynomialofadistanceregulargraph AT robertabeezer matchingpolynomialofadistanceregulargraph AT ejfarrell matchingpolynomialofadistanceregulargraph |