Distance-regular graphs with intersection arrays \(\{52, 35, 16; 1, 4, 28\}\) and \(\{69, 48, 24; 1, 4, 46\}\) do not exist. (English) Zbl 1245.05035
Summary: We prove that the arrays \(\{52, 35, 16; 1, 4, 28\}\) and \(\{69, 48, 24; 1, 4, 46\}\) cannot be realized as the intersection arrays of distance-regular graphs. In the proof we use some inequalities bounding the size of substructures (cliques, cocliques) in a distance-regular graph.
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