Distance-regular graphs with intersection arrays {52,35,16;1,4,28} and {69,48,24;1,4,46} do not exist
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.
distance-regular graph intersection array terwilliger graph