On a distance-regular graph with an intersection array {35,28,6;1,2,30}

It is proved that for a distance-regular graph Γ of diameter 3 with eigenvalue θ2=-1 the complement graph of Γ3 is pseudo-geometric for pGc3(k,b1/c2). Bang and Koolen investigated distance-regular graphs with intersection arrays (t+1)s,ts,(s+1-ψ);1,2,(t+1)ψ. If t=4, s=7, ψ=6 then we have array 35,28,6;1,2,30. Distance-regular graph Γ with intersection array {35,28,6;1,2,30} has spectrum of 351, 9168, -1182, -5273, v=1+35+490+98=624 vertices and Γ3 is a pseudogeometric graph for pG30(35,14). Due to the border of Delsarte, the order of clicks in Γ is not more than 8. It is also proved that either a neighborhood of any vertex in Γ is the union of an isolated 7-click, or the neighborhood of any vertex in Γ does not contain a 7-click and is a connected graph. The structure of the group G of automorphisms of a graph Γ with an intersection array {35,28,6;1,2,30} has been studied. In particular, π(G)⊆{2,3,5,7,13} and the edge symmetric graph Γ has a solvable group automorphisms.