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A note on girth-diameter cagesGabriela Araujo-Pardo,
Marston D. E. Conder,
Natalia García-Colín,
György Kiss,
Dimitri Leemans, 2025, izvirni znanstveni članek
Opis: 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.
Ključne besede: cages, girth, degree-diameter problem
Objavljeno v RUP: 10.06.2025; Ogledov: 88; Prenosov: 3
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