赋权图的基尔霍夫指标

Kirchhoff index in weighted graphs

通过对非赋权图的基尔霍夫指标计算公式Kf(G)=n sum from k=1 to n-1 1/(λ_k)适用范围的讨论,利用拉普拉斯矩阵的广义逆理论证明了该公式对于任意连通的赋权图成立,其中λ_k是赋权图的拉普拉斯矩阵的正特征值.

The applicable sPhere of Kirchhoff index Kf（G） was discussed, amplified and proved for any connected unweighted graphs. According to the theory of generalized inverse of Laplacian matrix we proved that this closed-form formulae Kf（G）=n∑^n-1 k=1 1/（λk） also held for any connected weighted graph that wasderived from the Laplacian spectrum of the weighted graphs.