特殊图类的Harmonic能量

Harmonic Energy of Specific Graphs

图G的Harmonic矩阵H(G)的特征值,即对应Harmonic特征多项式的根,表示为ρ1≥ρ2≥…≥ρn.Harmonic能量HE(G)为这n个特征值的绝对值之和.利用图的Harmonic能量的定义和性质,结合特殊图类的结构,给出了路图P_(n),圈图C_(n)的Harmonic特征多项式的递推公式,并给出了星图S_(n),完全图K_(n),完全二部图K_(m,n)的Harmonic能量的上界.

The eigenvalues of the Harmonic matrix H(G)for graph G,which are the roots of the Harmonic characteristic polynomial,are denoted byρ1≥ρ2≥…≥ρn.The Harmonic energy HE(G)of G is the sum of absolute values of n eigenvalues of H(G).By using the definition and properties of Harmonic energy of graphs and combining with the structures of them,the recurrence formula of the Harmonic characteristic polynomials of path graph P_(n),cycle graph C_(n) are analyzed.The upper bounds of Harmonic energy of the star graph S_(n),the complete graph Kn and the complete bipartite graph K_(m,n) are given.