A note on girth-diameter cagesAraujo-Pardo, Gabriela (Avtor) Conder, Marston D. E. (Avtor) García-Colín, Natalia (Avtor) Kiss, György (Avtor) Leemans, Dimitri (Avtor) cagesgirthdegree-diameter problemIn this paper we introduce a problem closely related to the Cage Problem and the Degree Diameter Problem. For integers k ≥ 2, g ≥ 3 and d ≥ 1, we define a (k; g, d)-graph to be a k-regular graph with girth g and diameter d. We denote by n₀(k; g, d) the smallest possible order of such a graph, and, if such a graph exists, we call it a (k; g, d)-cage. In particular, we focus on (k; 5, 4)-graphs. We show that n₀(k; 5, 4) ≥ k² + k + 2 for all k, and report on the determination of all (k; 5, 4)-cages for k = 3, 4 and 5 and of examples with k = 6, and describe some examples of (k; 5, 4)-graphs which prove that n₀(k; 5, 4) ≤ 2k² for infinitely many k.20252025-06-10 08:50:21Članek v reviji21342sl