Exact values of girth for some graphs D(k,q) and upper bounds of the order of cages

• Veröffentlicht in: Algebra and Discrete Mathematics
• Datum: 2008
• ISSN: 1726-3255
• 1. Verfasser: Pikuta, P.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут прикладної математики і механіки НАН України 2008
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/152392
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Exact values of girth for some graphs D(k,q) and upper bounds of the order of cages / P. Pikuta // Algebra and Discrete Mathematics. — 2008. — Vol. 7, № 2. — С. 83–88. — Бібліогр.: 13 назв. — англ.

Let q be a prime power and k∈{5,7,9,11}. In this paper it is shown that the girth of a graph D(k,q) is equal to k+5. As a consequence, explicit examples of graphs which provide the best known upper bounds of the order of (r,g)-cages, r≥5, g∈{10,14,16}, are given.