On the Nonexistence of Distance-Regular Graphs with Intersection Array $$ \{ 53,40,28,16; 1,4,10,28\}$$

Journal of Applied and Industrial Mathematics - We consider $$Q$$ -polynomial graphs of diameter $$4 $$ . Alongside the infinite series of intersection arrays $$ \{m(2m+1),(m-1)(2m+1),m^2, m;...     

On extensions of exceptional strongly regular graphs with eigenvalue 3

The study of distance-regular graphs in which neighborhoods of vertices are strongly regular graphs with eigenvalue 3 was initiated by Makhnev. In particular, he reduced these graphs to graphs in which neighborhoods of vertices are exceptional graphs or pseudogeometric graphs for pG _s?3(s, t). Makhnev and Paduchikh found parameters of exceptional graphs (see the proposition). In the present paper, we study amply regular graphs in which neighborhoods of vertices are exceptional strongly regular graphs with nonprincipal eigenvalue 3 and parameters from conditions 3–6 of the Proposition.     

Graphs in which the neighborhoods of vertices are pseudogeometric graphs for GQ(3, 5)

Doklady Mathematics -     

On automorphisms of strongly regular graphs with parameters (640, 243, 66, 108)

Doklady Mathematics -