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On the matching polynomials of graphs with small number of cycles of even length
Author(s) -
Yan Weigen,
Yeh YeongNan,
Zhang Fuji
Publication year - 2005
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.20670
Subject(s) - combinatorics , adjacency matrix , skew , mathematics , adjacency list , matching (statistics) , simple (philosophy) , graph , polynomial , discrete mathematics , computer science , telecommunications , philosophy , statistics , mathematical analysis , epistemology
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 ( G e ) of an arbitrary orientation G e of G and the minors of A ( G e ). 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, 2005