The Higher-Order Matching Polynomial of a Graph
ABSTRACT: 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) = [n/2] j=0 (−1)j p(G, j)xn−2j, called the matching polynomial of G, is closely related to the Hosoya index introduced in applications in physics an...
- Autores:
-
Estrada Valdés, Mario
Rada Rincón, Juan Pablo
Morales, Daniel A.
Araujo García, Oswaldo Rafael
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2005
- Institución:
- Universidad de Antioquia
- Repositorio:
- Repositorio UdeA
- Idioma:
- eng
- OAI Identifier:
- oai:bibliotecadigital.udea.edu.co:10495/44331
- Acceso en línea:
- https://hdl.handle.net/10495/44331
- Palabra clave:
- Polinomios
Polynomials
Funciones hipergeométricas
Functions, hypergeometric
Álgebra
Algebra
Índice de Hosoya
Polinomio de orden superior
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by/2.5/co/
| Summary: | ABSTRACT: 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) = [n/2] j=0 (−1)j p(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. |
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