线性四角链及四角莫比乌斯图的Kirchhoff指标

摘要

图G的Kirchhoff指标是指图G的所有点对之间的电阻距离之和。主要研究了线性四角链及四角莫比乌斯图的Kirchhoff指标。根据拉普拉斯多项式分解定理、Kirchhoff指标和拉普拉斯特征值之间的关系以及矩阵分解定理等得到线性四角链及四角莫比乌斯图的Kirchhoff指标计算公式；最后，通过举例直接利用欧姆定律所得Kirchhoff指标对所求公式加以验证。%The Kirchhoff index of G is the sum of resistance distances between all pairs of vertices in G. This pa-per studies the Kirchhoff index of linear tetragonal chains and tetragonal Moöbius graphs. According to the Lapla-cian polynomial decomposition theorem, the relationship between Kirchhoff index and the Laplacian eigenvalues, matrix decomposition theorem, this paper obtains formula for Kirchhoff index of linear tetragonal chains and te-tragonal Mo咬bius graphs. Finally, it verifies the formula using two examples whose Kirchhoff indexes are obtained from Ohm's law.