University of KashanIranian Journal of Mathematical Chemistry2228-64898120170301Relationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications7231509310.22052/ijmc.2017.15093ENF. TaghvaeeUniversity of KashanG. Fath-TabarUniversity of KashanJournal Article20160102ABSTRACT. 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.http://ijmc.kashanu.ac.ir/article_15093_be5ca1f23c477021c246d4c612236dc6.pdf