Resistance distance-based graph invariants of subdivisions and triangulations of graphs
Resistance distance-based graph invariants of subdivisions and triangulations of graphs
复制标题
图的细分和三角剖分的基于电阻距离的图不变量
DOI：
10.1016/j.dam.2014.08.039
复制
发表时间：
2015-01-30
影响因子：
1.1
通讯作者：
Klein, Douglas J.
中科院分区：
文献类型：
--
作者：
Yang, Yujun;Klein, Douglas J.
我们研究了三种基于电阻距离的图不变量：Kirchhoff指标，以及两种修正，即乘性度-Kirchhoff指标和加性度-Kirchhoff指标。最近，本文作者之一（2014）和Sun等人（2014）独立地获得了图的细分的Kirchhoff指数的（不同的）公式。Huang et al.（2014）处理了图的三角剖分的Kirchhoff指数。本文首先利用G的不变量，导出了剖分和三角剖分的加性度Kirchhoff指标和乘性度Kirchhoff指标的计算公式，以及三角剖分的Kirchhoff指标的一个新公式。然后，我们的Kirchhoffian图不变量之间的比较细分和三角剖分。最后给出了图的迭代剖分和三角剖分的图不变量的计算公式。(C)© 2014 Elsevier B. V.保留所有权利。
We study three resistance distance-based graph invariants: the Kirchhoff index, and two modifications, namely, the multiplicative degree-Kirchhoff index and the additive degree-Kirchhoff index. Recently, one of the present authors (2014) and Sun et al. (2014) independently obtained (different) formulas for the Kirchhoff index of subdivisions of graphs. Huang et al. (2014) treated the Kirchhoff index of triangulations of graphs. In our paper, first we derive formulae for the additive degree-Kirchhoff index and the multiplicative degree-Kirchhoff index of subdivisions and triangulations, as well as a new formula for the Kirchhoff index of triangulations, in terms of invariants of G. Then comparisons are made between each of our Kirchhoffian graph invariants for subdivision and triangulation. Finally, formulae for these graph invariants of iterated subdivisions and triangulations of graphs are obtained. (C) 2014 Elsevier B.V. All rights reserved.