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Bachratý, Martin; Šigiová, Jana and Širáň, Jozef
(2017).
DOI: https://doi.org/10.1142/s0219265917410110
Abstract
The largest order C(d,k) of a Cayley graph of degree d≥3 and diameter k≥2 cannot exceed the Moore bound M(d,k) the asymptotic form of which is M(d,k)=dk−O(dk−1) for d→∞ and a fixed k. The second and the third author and the three authors proved by direct constructions that the Moore bound for diameter k=2 and k=3, respectively, can be approached asymptotically by Cayley graphs in the sense that C(d,k)/M(d,k)→1 for some sequences of degrees d→∞. In this note we present a unifying principle underlying the two results, based on the existence of certain regular orbits of automorphism groups of suitable graphs.
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- Item ORO ID
- 62562
- Item Type
- Journal Item
- ISSN
- 1793-6713
- Keywords
- Degree-diameter problem; Cayley graph; Moore bound
- Academic Unit or School
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Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
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