1. A note on girth-diameter cagesGabriela Araujo-Pardo, Marston D. E. Conder, Natalia García-Colín, György Kiss, Dimitri Leemans, 2025, original scientific article Abstract: 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 k.
Keywords: cages, girth, degree-diameter problem
Published in RUP: 10.06.2025; Views: 80; Downloads: 1
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10. On the spectrum of the sizes of semiovals in PG (2,q), q oddGyörgy Kiss, Stefano Marcugini, Fernanda Pambianco, 2010, published scientific conference contribution Keywords: semiovals, projective planes, nontangent lines, bounds, secants
Published in RUP: 08.08.2016; Views: 3429; Downloads: 108
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