%0 Journal Article
%T Relationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications
%J Iranian Journal of Mathematical Chemistry
%I University of Kashan
%Z 2228-6489
%A Taghvaee, F.
%A Fath-Tabar, G.
%D 2017
%\ 03/01/2017
%V 8
%N 1
%P 7-23
%! Relationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications
%K Characteristic polynomial
%K Matching polynomial
%K Fullerene graph
%R 10.22052/ijmc.2017.15093
%X 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.
%U http://ijmc.kashanu.ac.ir/article_15093_be5ca1f23c477021c246d4c612236dc6.pdf