On the Integrability of Strongly Regular Graphs

被引：0
作者：
Jack H. Koolen
Masood Ur Rehman
Qianqian Yang
机构：
[1] University of Science and Technology of China,Wen
[2] University of Science and Technology of China,Tsun Wu Key Laboratory of CAS, School of Mathematical Sciences
来源：
Graphs and Combinatorics | 2019年 / 35卷
关键词：
Strongly regular graph; Lattice; -Integrability; 05C50; 05E30; 11H99;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Koolen et al. showed that if a connected graph with smallest eigenvalue at least -3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-3$$\end{document} has large minimal valency, then it is 2-integrable. In this paper, we will prove that a lower bound for the minimal valency is 166.
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页码：1273 / 1291
页数：18
相关论文
共 34 条
[1]  
Brouwer AE(1992)Structure and uniqueness of the Discret. Math. 106/107 77-82
[2]  
Haemers WH(1982) strongly regular graph Enumer. Des. 85 122-280
[3]  
Brouwer AE(1978)Strongly regular graphs and partial geometries J. Algebra 552 57-327
[4]  
van Lint JH(1976)Strongly regular graphs having strongly regular subconstituents J. Algebra 43 305-232
[5]  
Cameron PJ(1989)Line graphs, root systems and elliptic geometry Proc. R. Soc. Lond. Ser. A 426 211-8
[6]  
Goethals JM(1973)Low-dimensional lattices. V. Integral coordinates for integral lattices Philips Res. Rep. Suppl. 10 vi+-97-675
[7]  
Seidel JJ(1993)An algebraic approach to the association schemes of coding theory Congr. Numer. 94 3-158
[8]  
Cameron PJ(1969)Structure of the Hoffman–Singleton graph Trans. N Y Acad. Sci. 31 656-616
[9]  
Goethals JM(1975)The uniquence of Discret. Math. 12 143-12
[10]  
Seidel JJ(1995)The regular two-graph on Linear Algebra Appl. 226–228 593-165
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