A Group Commutator Involving the Last Distance Matrix and Dual Distance Matrix of a Q-Polynomial Distance-Regular Graph: The Hamming Graph Case

Mamart Siwaporn

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A Group Commutator Involving the Last Distance Matrix and Dual Distance Matrix of a Q-Polynomial Distance-Regular Graph: The Hamming Graph Case

机译：涉及Q-多项式距离常规图的最后距离矩阵和双距离矩阵的组换向器：汉明图案

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Let G denote the Hamming graph H(D, r) with r = 3. Consider the distance matrices {Ai}(i=0)(D) of Gamma. Fix a vertex x of Gamma, and consider the dual distance matrices {A(i)*}(i=0)(D) Gamma with respect to x. We investigate the group commutator A(D)(-1)A(D)*(-1)A(D)A(D)*. We show that this matrix is diagonalizable. We compute its eigenvalues and their eigenspaces. Let T denote the subconstituent algebra of Gamma with respect to x. We describe the action of A(D)(-1)A(D)*(-1)A(D)A(D)* on each irreducible T-module.

机译：设G表示具有R＆GT的汉明图H（d，r）; = 3.考虑伽马的距离矩阵{ai}（i = 0）（d）。修复伽马的顶点x，并考虑双距离矩阵{a（i）*}（i = 0）（d）伽马相对于x。我们研究了组换向器A（D）（ - 1）A（d）*（ - 1）a（d）a（d）*。我们表明该矩阵是对角线。我们计算其特征值和他们的eIgenspaces。设t表示γ的副间代数相对于x。我们描述了（D）（ - 1）A（d）*（ - 1）a（d）a（d）*在每个IRRAfible T模块上的作用。

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来源
《Graphs and combinatorics》 |2018年第4期|共15页
作者
Mamart Siwaporn;
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作者单位

Silpakorn Univ Fac Sci Dept Math Bangkok Thailand;

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原文格式 PDF
正文语种 eng
中图分类组合数学（组合学）;
关键词
Distance-regular graph; Q-polynomial; Distance matrix; Dual distance matrix;

机译：距离常规图;Q-多项式;距离矩阵;双距离矩阵;

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1. A Group Commutator Involving the Last Distance Matrix and Dual Distance Matrix of a Q-Polynomial Distance-Regular Graph: The Hamming Graph Case [J] . Mamart Siwaporn Graphs and combinatorics . 2018,第4期

机译：涉及Q-多项式距离常规图的最后距离矩阵和双距离矩阵的组换向器：汉明图案
2. On Q-polynomial distance-regular graphs Γ with strongly regular graphs ΓSUB2/SUB and ΓSUB3/SUB [J] . Belousov I. N., Makhnev A. A., Nirova M. S. Sibirskie elektronnye matematicheskie izvestiia: Siberian Electronic Mathematical Reports . 2019,第23期

机译：在具有强规则图Γ_{2 和Γ_{3 的Q多项式距离正则图Γ上}}
3. The Terwilliger polynomial of a Q-polynomial distance-regular graph and its application to pseudo-partition graphs [J] . Gavrilyuk Alexander L., Koolen Jack H. Linear Algebra and its Applications . 2015,第Null期

机译：Q多项式距离正则图的Terwilliger多项式及其在伪分区图上的应用
4. The Relation between the Square of the Adjacency Matrix and Spectra of the Distance Matrix of a Graph with Diameter Two [C] . Muhammad Yusuf, Kiki A. Sugeng Basic Science International Conference . 2018

机译：邻接矩阵的平方与直径两曲线图距离矩阵光谱的关系
5. Q-polynomial structures for association schemes and distance-regular graphs. [D] . Dickie, Garth A. 1995

机译：关联方案和距离正则图的Q多项式结构。
6. Eigenvalues of the resistance-distance matrix of complete multipartite graphs [O] . Kinkar Chandra Das, Yujun Yang -1

机译：完整多部分图的电阻距离矩阵的特征值
7. Dual Bipartite Q-polynomial Distance-regular Graphs [O] . Dickie Garth A., Terwilliger Paul M. 1996

机译：对偶二部Q多项式距离正则图
8. Graphs Cospectral with Distance-Regular Graphs [R] . Haemers, W. H., Spence, E. 1994

机译：带有距离正则图的光谱图

A Group Commutator Involving the Last Distance Matrix and Dual Distance Matrix of a Q-Polynomial Distance-Regular Graph: The Hamming Graph Case

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