On the matching polynomials of graphs with small number of cycles of even length
Authors:
- 1 January 2005
- journal article
- theoretical and-computational-developments
- Published by Wiley in International Journal of Quantum Chemistry
- Vol. 105 (2) , 124-130
Abstract
Suppose that G is a simple graph. We prove that if G contains a small number of cycles of even length then the matching polynomial of G can be expressed in terms of the characteristic polynomials of the skew adjacency matrix A(Ge) of an arbitrary orientation Ge of G and the minors of A(Ge). In addition to a formula previously discovered by Godsil and Gutman, we obtain a different formula for the matching polynomial of a general graph. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005Keywords
This publication has 20 references indexed in Scilit:
- Enumeration of perfect matchings of graphs with reflective symmetry by PfaffiansAdvances in Applied Mathematics, 2004
- On the Matching Spectrum of RotagraphsZeitschrift für Naturforschung A, 1985
- On the construction of a hermitean matrix associated with the acyclic polynomial of a conjugated hydrocarbonChemical Physics Letters, 1981
- On the theory of the matching polynomialJournal of Graph Theory, 1981
- An introduction to matching polynomialsJournal of Combinatorial Theory, Series B, 1979
- Perturbation-graph theory—ITetrahedron, 1978
- Graph Theory with Applications1976
- A characterization of convertible (0, 1)-matricesJournal of Combinatorial Theory, Series B, 1975
- General properties of polymer systemsCommunications in Mathematical Physics, 1971
- Location of the zeros of the partition function for some classical lattice systemsPhysics Letters A, 1970