378 KB0 KB217 KB2025Araujo-Pardo, GabrielaConder, Marston D. E.García-Colín, NataliaKiss, GyörgyLeemans, Dimitrištevilka:3, article p3.06letnik:8str. 1-7DOI:10.26493/2590-9770.1743.19fCOBISSID_HOST:238839043ISSN:2590-9770URN:URN:NBN:SI:doc-1SK2M1ZUenFakulteta za matematiko, naravoslovje in informacijske tehnologijeThe art of discrete and applied mathematicscagesdegree-diameter problemgirthA note on girth-diameter cages|In 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 kTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije