Full proof of the existence of a degree 8 circulant graph of order L(8,k) of arbitrary diameter k

Lewis, Robert (2014). Full proof of the existence of a degree 8 circulant graph of order L(8,k) of arbitrary diameter k. arXiv.

URL: https://arxiv.org/abs/1404.3949

Abstract

This is the full proof of Theorem 3 in the paper "The degree-diameter problem for circulant graphs of degree 8 and 9" by the author. To avoid the paper being unduly long it includes only the exceptions for the orthant of v₁ for diameter k≡0 (mod 2) and for k≡1 (mod 2). In the version below the exceptions for all eight orthants for diameter k≡0 and k≡1 (mod 2) are included in full. This proof closely follows the approach taken by Dougherty and Faber in their proof of the existence of the degree 6 graph of order DF(6, k) for all diameters k≥2.

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About

• Item ORO ID
• 47737
• Item Type
• Other - Other
• Extra Information
• An abridged version of this paper was published in the Electronic Journal of Combinatorics in 2014. This paper contains the full proof of this theorem.
• Keywords
• degree-diameter; extremal; circulant graphs; Abelian Cayley graphs
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2014 Robert Lewis
• Related URLs
• • http://www.combinatorics.org/ojs/index.p...(Other)
• Depositing User
• Robert Lewis