Download this article
Download this article For screen
For printing
Recent Issues
Volume 13, Issue 2
Volume 13, Issue 1
Volume 12, Issue 4
Volume 12, Issue 3
Volume 12, Issue 2
Volume 12, Issue 1
Volume 11, Issue 4
Volume 11, Issue 3
Volume 11, Issue 2
Volume 11, Issue 1
Volume 10, Issue 4
Volume 10, Issue 3
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 4
Volume 9, Issue 3
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
Older Issues
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 2-3
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 1-2
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 3-4
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
founded and published with the
scientific support and advice of
mathematicians from the
Moscow Institute of
Physics and Technology
Subscriptions
 
ISSN (electronic): 2996-220X
ISSN (print): 2996-2196
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
On distance graphs in rational spaces

Artemy A. Sokolov
Vol. 12 (2023), No. 2, 165–173
DOI: 10.2140/moscow.2023.12.165
Abstract

For any positive definite rational quadratic form q of n variables let G(ℚn,q) denote the graph with vertices ℚn and x,y ∈ ℚn connected if and only if q(x − y) = 1. This notion generalises standard Euclidean distance graphs. In this article we study these graphs and show how to find the exact value of clique number of the G(ℚn,q).

We also prove rational analogue of the Beckman–Quarles theorem that any unit-preserving bijection of ℚn onto itself is an isometry.

PDF Access Denied

We have not been able to recognize your IP address 3.149.236.96 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
Euclidean distance graph, rational points, quadratic form, clique, regular simplex, Beckman–Quarles theorem
Mathematical Subject Classification
Primary: 05C60, 05C69, 52C35
Milestones
Received: 3 March 2023
Revised: 4 April 2023
Accepted: 18 April 2023
Published: 4 June 2023
Authors
Artemy A. Sokolov
Department of Discrete Mathematics
Moscow Institute of Physics and Technology
Dolgoprudny
Russia
© 2023 MSP (Mathematical Sciences Publishers).