Taghvaee, F., Fath-Tabar, G. (2017). Relationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications. Iranian Journal of Mathematical Chemistry, 8(1), 7-23. doi: 10.22052/ijmc.2017.15093

F. Taghvaee; G. Fath-Tabar. "Relationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications". Iranian Journal of Mathematical Chemistry, 8, 1, 2017, 7-23. doi: 10.22052/ijmc.2017.15093

Taghvaee, F., Fath-Tabar, G. (2017). 'Relationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications', Iranian Journal of Mathematical Chemistry, 8(1), pp. 7-23. doi: 10.22052/ijmc.2017.15093

Taghvaee, F., Fath-Tabar, G. Relationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications. Iranian Journal of Mathematical Chemistry, 2017; 8(1): 7-23. doi: 10.22052/ijmc.2017.15093

Relationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications

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.

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