Using equality in the Krein conditions to prove nonexistence of certain distance-regular graphs

摘要

We prove the nonexistence of a distance-regular graph with intersection array {74, 54, 15; 1, 9, 60} and of distance-regular graphs with intersection arrays {4r(3) + 8r(2) + 6r + 1, 2r(r + 1)(2r + 1), 2r(2) + 2r + 1; 1, 2r(r + 1), (2r + 1)(2r(2) + 2r + 1)} with r an integer and r >= 1. Both cases serve to illustrate a technique which can help in determining structural properties for distance-regular graphs and association schemes with a sufficient number of vanishing Krein parameters. (C) 2007 Elsevier Inc. All rights reserved.