Resistance distance and Kirchhoff index in circulant graphs
Resistance distance and Kirchhoff index in circulant graphs
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DOI：
10.1002/qua.21068
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发表时间：
2007
影响因子：
2.2
通讯作者：
Heping Zhang;Yujun Yang
中科院分区：
文献类型：
--
作者：
Heping Zhang;Yujun Yang
通过用单位电阻代替G的每条边，计算连通(分子)图G的顶点i和j之间的电阻距离Rij，作为由G构成的相应网络中节点i和j之间的有效电阻。基尔霍夫指数KF(G)是所有顶点对之间的阻力距离之和。利用拉普拉斯谱和特征向量，给出了循环图的Kirchhoff指数和阻力距离的闭合公式。还给出了完全图、完全图、圈、Mobius阶梯MP�四类循环图的特殊公式。尤其是，
The resistance distance rij between vertices i and j of a connected (molecular) graph G is computed as the effective resistance between nodes i and j in the corresponding network constructed from G by replacing each edge of G with a unit resistor. The Kirchhoff index Kf (G) is the sum of resistance distances between all pairs of vertices. In this work, closed-form formulae for Kirchhoff index and resistance distances of circulant graphs are derived in terms of Laplacian spectrum and eigenvectors. Special formulae are also given for four classes of circulant graphscomplete graphs, complete graphs minus a perfect matching, cycles, Mobius ladders Mp � . In particular, the