Bipartite graphs with five eigenvalues and pseudo designs
نویسنده
چکیده
A pseudo (v, k, λ)-design is a pair (X,B), where X is a v-set, and B = {B1, . . . ,Bv−1} is a collection of k-subsets (blocks) of X such that any two distinct Bi,Bj intersect in λ elements, and 0 ≤ λ < k ≤ v−1. We use the notion of pseudo designs to characterize graphs of order n whose (adjacency) spectrum contains zero and ±θ with multiplicity (n− 3)/2 where 0 < θ ≤√2. Meanwhile, partial results confirming a conjecture of O. Marrero on a characterization of pseudo (v, k, λ)-designs are obtained.
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