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 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| 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| Summary: | 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. |
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