On the characterization of the folded halved cubes by their intersection arrays
type: Item
instance of: scholarly article
title: On the characterization of the folded halved cubes by their intersection arrays
zbMATH Open document ID: 1038.05060
DOI: 10.1023/A:1024116811689
published in: Designs, Codes and Cryptography
publication date: 2003-08-21T00:00:00Z
review text: A folded halved \(2m\)-cube is a distance-regular graph with intersection array \(\{b_0, b_1,\dots, b_{d-1}\); \(c_1, c_2,\dots, c_d\}\) such that \(d:= \lfloor{m\over 2}\rfloor\) and \[ \begin{gathered} b_i= (m- i)(2m- 2i- 1),\quad c_i= i(2i- 1)\qquad (0\leq i\leq d-1),\\ c_d= \begin{cases} d(2d- 1),\quad &\text{if }m\text{ is odd};\\ 2d(2d- 1),\quad &\text{if }m\text{ is even}.\end{cases}\end{gathered} \] The paper shows that the folded halved cubes of diameter \(d\geq 5\) and the larger folded halved cube of diameter 4 are uniquely determined by their intersection arrays. The result also suggests a characterization of all pseudo-partition graphs of diameter \(d\geq 5\).
reviewed by: R. E. L. Aldred
Mathematics Subject Classification ID: 05E30
zbMATH DE Number: 1968869
zbMATH Keywords: distance-regular graph
author: Klaus Metsch
MaRDI profile type: Publication
full work available at URL: a:1024116811689
OpenAlex ID: W134434485
description: scientific article; zbMATH DE number 1968869