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  • A note on girth-diameter cages [Elektronski vir]
    Araujo-Pardo, Gabriela ...
    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.
    Vir: The art of discrete and applied mathematics [Elektronski vir]. - ISSN 2590-9770 (Vol. 8, no. 3, [article no.] P3.06, 2025, str. 1-7)
    Vrsta gradiva - e-članek ; neleposlovje za odrasle
    Leto - 2025
    Jezik - angleški
    COBISS.SI-ID - 238839043

    Povezava(-e):

    https://adam-journal.eu/index.php/ADAM/article/view/1743
    Repozitorij Univerze na Primorskem - RUP
    DOI

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