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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