设v1,v2,…,vn是n阶图G的顶点,d(vi)表示顶点vi的度.如果(d(v1),d(v2),…,d(vn))T是图G的邻接矩阵的一个特征向量,则说图G是调和的.证明了恰有一个4-调和5圈图,结合文献[6],确定了所有调和的5圈图.
A graph G with n vertices v1 , v2, …, vn is said to be harmonic if the degree sequence ( d( v1 ), d( v2 ), …, d per, all pentacyclic harmonic graphs are determined.