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

• 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
• Journal Title: Algebra and Discrete Mathematics

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 \...