The higher-order matching polynomial of a graph
Given a graph G with n vertices, let p(G,j) denote the number of ways j mutually nonincident edges can be selected in G. The polynomial M(x)=∑j=0[n/2](−1)jp(G,j)xn−2j, called the matching polynomial of G, is closely related to the Hosoya index introduced in applications in physics and chemistry. In...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.1565 |
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| _version_ | 1832560988836069376 |
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| author | Oswaldo Araujo Mario Estrada Daniel A. Morales Juan Rada |
| author_facet | Oswaldo Araujo Mario Estrada Daniel A. Morales Juan Rada |
| author_sort | Oswaldo Araujo |
| collection | DOAJ |
| description | Given a graph G with n vertices, let p(G,j) denote the number of ways j mutually nonincident edges can be selected in G. The polynomial M(x)=∑j=0[n/2](−1)jp(G,j)xn−2j, called the matching polynomial of G, is closely related to the Hosoya index introduced in applications in physics and chemistry. In this work we generalize this polynomial by introducing the number of
disjoint paths of length t, denoted by pt(G,j). We compare this higher-order matching polynomial with the usual one,
establishing similarities and differences. Some interesting examples are given. Finally, connections between our generalized matching polynomial and hypergeometric functions are found. |
| format | Article |
| id | doaj-art-010db34699e74ee7a31cffbdace6396a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-010db34699e74ee7a31cffbdace6396a2025-02-03T01:26:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005101565157610.1155/IJMMS.2005.1565The higher-order matching polynomial of a graphOswaldo Araujo0Mario Estrada1Daniel A. Morales2Juan Rada3Departamento de Matemáticas, Facultad de Ciencias, Universidad de Los Andes, Mérida 5101, VenezuelaICIMAF, La Habana, CubaFacultad de Ciencias, Universidad de Los Andes, Apartado Postal A61, La Hechicera, Mérida 5101, VenezuelaDepartamento de Matemáticas, Facultad de Ciencias, Universidad de Los Andes, Mérida 5101, VenezuelaGiven a graph G with n vertices, let p(G,j) denote the number of ways j mutually nonincident edges can be selected in G. The polynomial M(x)=∑j=0[n/2](−1)jp(G,j)xn−2j, called the matching polynomial of G, is closely related to the Hosoya index introduced in applications in physics and chemistry. In this work we generalize this polynomial by introducing the number of disjoint paths of length t, denoted by pt(G,j). We compare this higher-order matching polynomial with the usual one, establishing similarities and differences. Some interesting examples are given. Finally, connections between our generalized matching polynomial and hypergeometric functions are found.http://dx.doi.org/10.1155/IJMMS.2005.1565 |
| spellingShingle | Oswaldo Araujo Mario Estrada Daniel A. Morales Juan Rada The higher-order matching polynomial of a graph International Journal of Mathematics and Mathematical Sciences |
| title | The higher-order matching polynomial of a graph |
| title_full | The higher-order matching polynomial of a graph |
| title_fullStr | The higher-order matching polynomial of a graph |
| title_full_unstemmed | The higher-order matching polynomial of a graph |
| title_short | The higher-order matching polynomial of a graph |
| title_sort | higher order matching polynomial of a graph |
| url | http://dx.doi.org/10.1155/IJMMS.2005.1565 |
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