Abstract
Abstract There exist well-known distance-regular graphs Γ of diameter 3 for which Γ 3 is a triangle-free graph. An example is given by the Johnson graph J (8, 3) with the intersection array {15, 8, 3;1, 4, 9}. The paper is concerned with the problem of the existence of distance-regular graphs Γ with the intersection arrays {78, 50, 9;1, 15, 60} and {174, 110, 18;1, 30, 132} for which Γ 3 is a triangle-free graph.
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