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In this paper, we shall first describe the theory of distance-regular graphs and then apply it to the classification of Moore graphs. The object of the paper is to prove that there are no Moore graphs (other than polygons) of diameter ≥ 3. An independent proof of this result has been given by Barmai and Ito(1). Taken with the result of (4), this shows that the only possible Moore graphs are the following:

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Functions with bounded variation and with a (total) variation are examined within Bishop's constructive mathematics. It is shown that the property of having a variation is hereditary downward on compact intervals, and hence that a real‐valued function f with a variation on a compact interval can be expressed as a difference of two increasing functions. Moreover, if f is sequentially continuous, then the corresponding variation function, and hence f itself, is uniformly continuous. 1991 Mathematics Subject Classification 26A45.