设v1,v2,v3,…,vn是图G的n个顶点,若(d(v1),d(v2),d(v3),…d(vn))^T是图G邻接矩阵A的特征向量,则称G是调和图,其中d(vi)表示顶点vi的度.1—5圈的调和图已经确定,这里确定了所有的6-圈调和图.
A graph G on n vertice v1, v2, v3, …, vn is said to be harmonic if ( d( v1 ), d(v2), d( v3),… d( vn) )^T is an eigenvector of its adjacency matrix A , where d( vi) is the degree of the vertex vi, i = 1,2,3,…, n. Earlier all unicyclic, acyclic, bicyclic, tricyclic tetracyclic and pentacyclic harmonic graphs were determined. In this paper, we determined all hexacyclic harmonic graphs.