Resistance distance-based graph invariants and the number of spanning trees of linear crossed octagonal graphs
Resistance distance-based graph invariants and the number of spanning trees of linear crossed octagonal graphs
复制标题
基于电阻距离的图不变量和线性交叉八边形图的生成树数量
DOI：
10.1007/s12190-019-01306-6
复制
发表时间：
2019-11-21
影响因子：
2.2
通讯作者：
Hayat, Sakander
中科院分区：
文献类型：
--
作者：
Zhao, Jing;Liu, Jia-Bao;Hayat, Sakander
电阻距离是一种新的距离函数，也是一种新的本征图度量，它是对普通距离的一些推广。设是一个线性交叉八边形图。最近，Pan和Li（Int J Quantum Chem 118（24）：e25787，2018）推导了Kirchhoff指数，乘法度-Kirchhoff指数和生成树数的封闭公式。他们指出，给出的Kirchhoff指数和乘法度Kirchhoff指数的显式公式是有趣的。受此启发，本文研究了两种基于电阻距离的图不变量，即Kirchhoff指标和乘性度-Kirchhoff指标。我们首先确定拉普拉斯算子（分别为规范化拉普拉斯算子）的公式光谱进一步给出了这两种基于电阻距离的图不变量和生成树的计算公式。更令人惊讶的是，我们发现，基尔霍夫（乘法度基尔霍夫，resp.）指数几乎是四分之一维纳（古特曼，分别）线性交叉八边形图的指数
Resistance distance is a novel distance function, also a new intrinsic graph metric, which makes some extensions of ordinary distance. Letbe a linear crossed octagonal graph. Recently, Pan and Li (Int J Quantum Chem 118(24):e25787, 2018) derived the closed formulas for the Kirchhoff index, multiplicative degree-Kirchhoff index and the number of spanning trees of. They pointed that it is interesting to give the explicit formulas for the Kirchhoff and multiplicative degree-Kirchhoff indices of. Inspired by these, in this paper, two resistance distance-based graph invariants, namely, Kirchhoff and multiplicative degree-Kirchhoff indices are studied. We firstly determine formulas for the Laplacian (normalized Laplacian, resp.) spectrum of. Further, the formulas for those two resistance distance-based graph invariants and spanning trees are given. More surprising, we find that the Kirchhoff (multiplicative degree-Kirchhoff, resp.) index is almost one quarter to Wiener (Gutman, resp.) index of a linear crossed octagonal graph.