Institute of Mathematics and Mechanics, Ural Division, Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620219, Russian Federation

摘要

The distance regular graphs in which the neighborhoods of vertices are isomorphic to the Gewirtz graph is discussed. The Gewirtz graph is the only strongly regular graph with parameters (56, 10, 0, 2). The theorem is proved by Higman's method for automorphisms of a distance regular graph. An irreducible rational representation is a rational representation that is irreducible over the field of rational numbers.