Exact values of girth for some graphs \(D\left({k},{q}\right)\) and upper bounds of the order of cages

Exact values of girth for some graphs \(D\left({k},{q}\right)\) and upper bounds of the order of cages

Let \(q\) be a prime power and \(k \in \left\{5,7,9,11\right\}\). In this paper it is shown that the girth of a graph \(D\left(k,q\right)\) is equal to \(k + 5\). As a consequence, explicit examples of graphs which provide the best known upper bounds of the order of \(\left(r,g\right)\)-cages, \(r \...

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Date:2018
Main Author: Pikuta, Piotr
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2018
Subjects:
Girth
Cages
Extremal
05C35
05C38
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/810
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id oai:ojs.admjournal.luguniv.edu.ua:article-810
record_format ojs
spelling oai:ojs.admjournal.luguniv.edu.ua:article-8102018-03-22T09:39:19Z Exact values of girth for some graphs \(D\left({k},{q}\right)\) and upper bounds of the order of cages Pikuta, Piotr Girth, Cages, Extremal 05C35, 05C38 Let \(q\) be a prime power and \(k \in \left\{5,7,9,11\right\}\). In this paper it is shown that the girth of a graph \(D\left(k,q\right)\) is equal to \(k + 5\). As a consequence, explicit examples of graphs which provide the best known upper bounds of the order of \(\left(r,g\right)\)-cages, \(r \geq 5\), \(g \in \left\{10,14,16\right\}\), are given. Lugansk National Taras Shevchenko University 2018-03-22 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/810 Algebra and Discrete Mathematics; Vol 7, No 2 (2008) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/810/340 Copyright (c) 2018 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2018-03-22T09:39:19Z
collection OJS
language English
topic Girth
Cages
Extremal
05C35
05C38
spellingShingle Girth
Cages
Extremal
05C35
05C38
Pikuta, Piotr
Exact values of girth for some graphs \(D\left({k},{q}\right)\) and upper bounds of the order of cages
topic_facet Girth
Cages
Extremal
05C35
05C38
format Article
author Pikuta, Piotr
author_facet Pikuta, Piotr
author_sort Pikuta, Piotr
title Exact values of girth for some graphs \(D\left({k},{q}\right)\) and upper bounds of the order of cages
title_short Exact values of girth for some graphs \(D\left({k},{q}\right)\) and upper bounds of the order of cages
title_full Exact values of girth for some graphs \(D\left({k},{q}\right)\) and upper bounds of the order of cages
title_fullStr Exact values of girth for some graphs \(D\left({k},{q}\right)\) and upper bounds of the order of cages
title_full_unstemmed Exact values of girth for some graphs \(D\left({k},{q}\right)\) and upper bounds of the order of cages
title_sort exact values of girth for some graphs \(d\left({k},{q}\right)\) and upper bounds of the order of cages
description Let \(q\) be a prime power and \(k \in \left\{5,7,9,11\right\}\). In this paper it is shown that the girth of a graph \(D\left(k,q\right)\) is equal to \(k + 5\). As a consequence, explicit examples of graphs which provide the best known upper bounds of the order of \(\left(r,g\right)\)-cages, \(r \geq 5\), \(g \in \left\{10,14,16\right\}\), are given.
publisher Lugansk National Taras Shevchenko University
publishDate 2018
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/810
work_keys_str_mv AT pikutapiotr exactvaluesofgirthforsomegraphsdleftkqrightandupperboundsoftheorderofcages
first_indexed 2025-07-17T10:31:37Z
last_indexed 2025-07-17T10:31:37Z
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