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This is the full proof of Theorem 3 on the existence of the largest knowndegree 8 circulant graph for all diameters stated in the paper "Thedegree-diameter problem for circulant graphs of degree 8 and 9" by the author.To avoid the paper being unduly long the exceptions for only one case wereincluded in the statement of the proof. In the statement of the proof presentedin this paper the exceptions for all cases are included in full. This proofclosely follows the approach taken by Dougherty and Faber for the existence ofthe largest known degree 6 circulant graph for all diameters.

Full Proof of the Existence of a Degree 8 Circulant graph of Order L(8,k) of Arbitrary Diameter k