The Number Of Matchings Of Low Order In Hexagonal Systems

Abstract

. A simple way to calculate the number of k-matchings, k 5, in hexagonal systems is presented. Some relations between the coefficients of the characteristic polynomial of the adjacency matrix of a hexagonal system and the number of matchings are obtained. 1. Introduction A hexagonal system is a 2-connected plane graph G such that every interior face of G is a regular hexagon. A k-matching (or a matching of order k) of a graph G is a set of k pairwise nonadjacent edges of G. A hexagonal system has only vertices of degree 2 or 3. Note also that each hexagonal system H is a bipartite graph. It is also easy to see that H does not contain cycles of lengths 4; 8. Let G be a hexagonal system. Throughout the paper, n will denote the number of vertices whereas m will stand for the number of edges of G. By A = fa ij g n i;j=1 we will denote the adjacency matrix of G, that is a ij = ae 0; ij = 2 E (G) 1; ij 2 E (G) : Since every hexagonal system is bipartite, coefficients of the characte..