@article {
author = {Taghvaee, F. and Fath-Tabar, G.},
title = {Relationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {8},
number = {1},
pages = {7-23},
year = {2017},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2017.15093},
abstract = {ABSTRACT. Suppose G is a graph, A(G) its adjacency matrix and f(G, x)=x^n+a_(n-1)x^(n-1)+... is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = x^n-m(G,1)x^(n-2) + ... where m(G,k) is the number of k-matchings in G. In this paper, we determine the relationship between 2k-th coefficient of characteristic polynomial, a_(2k), and k-th coefficient of matching polynomial, (-1)^km(G, k), in a regular graph. In the rest of this paper, we apply these relations for finding 5,6-matchings of fullerene graphs.},
keywords = {Characteristic polynomial,Matching polynomial,Fullerene graph},
url = {https://ijmc.kashanu.ac.ir/article_15093.html},
eprint = {https://ijmc.kashanu.ac.ir/article_15093_be5ca1f23c477021c246d4c612236dc6.pdf}
}