Resistance distance-based graph invariants of subdivisions and triangulations of graphs

被引：50
作者：
Yang, Yujun [1 ]
Klein, Douglas J. [2 ]
机构：
[1] Yantai Univ, Sch Math & Informat Sci, Yantai 264005, Shandong, Peoples R China
[2] Texas A&M Univ, Dept Marine Sci, Galveston, TX 77553 USA
来源：
DISCRETE APPLIED MATHEMATICS | 2015年 / 181卷
基金：
中国博士后科学基金; 美国国家科学基金会;
关键词：
Resistance distance; Kirchhoff index; Subdivision; Triangulation; Additive degree-Kirchhoff index; Multiplicative degree-Kirchhoff index; DEGREE KIRCHHOFF INDEX; WIENER INDEX; SZEGED INDEX; LOWER BOUNDS; IN-LINE; FORMULA;
D O I：
10.1016/j.dam.2014.08.039
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：260 / 274
页数：15
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