Distance-regular graphs with intersectuion arrays {42,30,12;1,6,28} and {60,45,8;1,12,50} do not exist

摘要

Koolen and Park obtained the list of intersection arrays for Shilla graphs with b = 3. In particular distance-regular graph with intersectuion array {42, 30, 12; 1, 6, 28} is Shilla graphs with b = 3. Gavri- lyuk and Makhnev investigated properties of a graph with intersectuion array {60, 45, 8; 1, 12, 50}. We proved that distance-regular graphs with intersectuion arrays {42, 30, 12; 1, 6, 28} and {60, 45, 8; 1, 12, 50} do not exist.