... taken with multiplicity 2. Crooked Functions, Bent Functions, and Distance Regular GraphsT.D. Bending D. Fon-Der-FlaassSchool of Mathematical Sciences,Queen Mary and Westfield College, London ... {(a, i, α)}; vertices(a, i, α )and( b, j, β) are adjacent if and only if they are distinct, and α + β = D(a, i; b, j).PROPOSITION 13 The graph GQis distance regular with intersection array(2n+1− ... and Moorhouse. We study graph-theoretical properties ofthe resulting graphs, including their automorphisms. Also we demonstrate aconnection between crooked functions and bent functions.1 Crooked...