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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| Дата: | 2018 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/810 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543361619460096 |
|---|---|
| author | Pikuta, Piotr |
| author_facet | Pikuta, Piotr |
| author_sort | Pikuta, Piotr |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-03-22T09:39:19Z |
| 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. |
| first_indexed | 2026-02-08T07:58:06Z |
| format | Article |
| id | admjournalluguniveduua-article-810 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:58:06Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| 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 |
| title | 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_short | 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 |
| topic | Girth Cages Extremal 05C35 05C38 |
| topic_facet | Girth Cages Extremal 05C35 05C38 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/810 |
| work_keys_str_mv | AT pikutapiotr exactvaluesofgirthforsomegraphsdleftkqrightandupperboundsoftheorderofcages |