Kirchhoff index of linear hexagonal chains
Kirchhoff index of linear hexagonal chains
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DOI：
10.1002/qua.21537
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发表时间：
2008
影响因子：
2.2
通讯作者：
Yujun Yang;Heping Zhang
中科院分区：
文献类型：
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作者：
Yujun Yang;Heping Zhang
连通（分子）图G的顶点i和j之间的电阻距离rij计算为由G构建的相应网络中节点i和j之间的有效电阻，通过将G的每条边替换为一个单位电阻。基尔霍夫指数Kf(G)是所有顶点对之间的电阻距离之和。本文根据拉普拉斯多项式的分解定理，得到了线性六方链Ln的拉普拉斯谱由路径P2n+1的拉普拉斯谱和2n+1阶对称三对角矩阵的特征值组成。利用上述矩阵特征多项式的根与系数之间的关系，导出了用拉普拉斯谱表示的Ln的Kirchhoff指数的显式封闭公式。令我们惊讶的是，Ln的克里希霍夫指数大约是它的维纳指数的一半。最后，我们证明了在包含Ln的一类图中，对所有图G都成立。©2007 Wiley期刊公司量子化学学报，2008
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, according to the decomposition theorem of Laplacian polynomial, we obtain that the Laplacian spectrum of linear hexagonal chain Ln consists of the Laplacian spectrum of path P2n+1 and eigenvalues of a symmetric tridiagonal matrix of order 2n + 1. By applying the relationship between roots and coefficients of the characteristic polynomial of the above matrix, explicit closed-form formula for Kirchhoff index of Ln is derived in terms of Laplacian spectrum. To our surprise, the Krichhoff index of Ln is approximately to one half of its Wiener index. Finally, we show that holds for all graphs G in a class of graphs including Ln. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008