Matchings in hexagonal cacti
Explicit recurrences are derived for the matching polynomials of the basic types of hexagonal cacti, the linear cactus and the star cactus and also for an associated graph, called the hexagonal crown. Tables of the polynomials are given for each type of graph. Explicit formulae are then obtained for...
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| Format: | Article |
| Language: | English |
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Wiley
1987-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171287000395 |
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| _version_ | 1832561645826605056 |
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| author | E. J. Farrell |
| author_facet | E. J. Farrell |
| author_sort | E. J. Farrell |
| collection | DOAJ |
| description | Explicit recurrences are derived for the matching polynomials of the basic types of hexagonal cacti, the linear cactus and the star cactus and also for an associated graph, called the hexagonal crown. Tables of the polynomials are given for each type of graph. Explicit formulae are then obtained for the number of defect-d matchings in the graphs, for various values of d. In particular, formulae are derived for the number of perfect matchings in all three types of graphs. Finally, results are given for the total number of matchings in the graphs. |
| format | Article |
| id | doaj-art-7927b115c30e4aa7857e11d1393f7a88 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1987-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-7927b115c30e4aa7857e11d1393f7a882025-02-03T01:24:30ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251987-01-0110232133810.1155/S0161171287000395Matchings in hexagonal cactiE. J. Farrell0Department of Mathematics, The University of the West Indies, St. Augustine, Trinidad and TobagoExplicit recurrences are derived for the matching polynomials of the basic types of hexagonal cacti, the linear cactus and the star cactus and also for an associated graph, called the hexagonal crown. Tables of the polynomials are given for each type of graph. Explicit formulae are then obtained for the number of defect-d matchings in the graphs, for various values of d. In particular, formulae are derived for the number of perfect matchings in all three types of graphs. Finally, results are given for the total number of matchings in the graphs.http://dx.doi.org/10.1155/S0161171287000395cactuschainshexagonlinear cactusstar cactushexagonal crownmatchingmatching polynomialsdefect-d matchingperfect matchinggeneratin functionrecurrence relation. |
| spellingShingle | E. J. Farrell Matchings in hexagonal cacti International Journal of Mathematics and Mathematical Sciences cactus chains hexagon linear cactus star cactus hexagonal crown matching matching polynomials defect-d matching perfect matching generatin function recurrence relation. |
| title | Matchings in hexagonal cacti |
| title_full | Matchings in hexagonal cacti |
| title_fullStr | Matchings in hexagonal cacti |
| title_full_unstemmed | Matchings in hexagonal cacti |
| title_short | Matchings in hexagonal cacti |
| title_sort | matchings in hexagonal cacti |
| topic | cactus chains hexagon linear cactus star cactus hexagonal crown matching matching polynomials defect-d matching perfect matching generatin function recurrence relation. |
| url | http://dx.doi.org/10.1155/S0161171287000395 |
| work_keys_str_mv | AT ejfarrell matchingsinhexagonalcacti |