增强超立方体剖分图和全图的基尔霍夫指标
Kirchhoff Index in Subdivision and Total Graphs of Enhanced Hypercube
DOI: 10.12677/AAM.2019.84078, PDF,   
作者: 许 萍：新疆大学数学与系统科学学院，新疆 乌鲁木齐
关键词: 增强超立方体；基尔霍夫指标；电阻距离；Enhanced Hypercube； Kirchhoff Index； Resistance Distance
摘要: 图G任意两个顶点之间的电阻距离指的是它们之间的网络有效电阻，如果将图G的每一条边都用一个单位电阻代替，图G的基尔霍夫指标指的是图G的所有点对之间电阻距离之和。在本文中，我们通过推导增强超立方体网络Qn,k和它的两个变型网络s(Qn,k)和t(Qn,k)的拉普拉斯特征多项式的关系，从而得到了增强超立方体网络Qn,k和它的两个变型网络(Qn,k)和t(Qn,k)的基尔霍夫指标的关系。同时，我们还分别得到了s(Qn,k)和t(Qn,k)的具体的基尔霍夫指标公式。
Abstract: The resistance distance between any two vertices of G is defined as the network effective resistance between them if each edge of G is replaced by a unit resistor. The Kirchhoff index Kf(G) is the sum of the resistance distances between all the pairs of vertices in G. In this paper, we obtained the relationship of Kirchhoff index between enhanced hypercube networks Qn,k and its two variant networks s(Qn,k) and t(Qn,k), by deducing the characteristic polynomial of the Laplacian matrix related networks. Meanwhile, the special formulas for the Kirchhoff indexes of s(Qn,k) and t(Qn,k) were proposed, respectively.
文章引用：许萍. 增强超立方体剖分图和全图的基尔霍夫指标[J]. 应用数学进展, 2019, 8(4): 691-696. https://doi.org/10.12677/AAM.2019.84078

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