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

• Дата: 2018
• Автор: Pikuta, Piotr
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Lugansk National Taras Shevchenko University 2018
• Теми: Girth; Cages; Extremal; 05C35; 05C38
• Онлайн доступ: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/810
• Назва журналу: 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 \...