Distance-regular graphs with an eigenvalue
نویسنده
چکیده
It is known that bipartite distance-regular graphs with diameter D > 3, valency k > 3, intersection number c2 > 2 and eigenvalues k = θ0 > θ1 > · · · > θD satisfy θ1 6 k− 2 and thus θD−1 > 2− k. In this paper we classify non-complete distanceregular graphs with valency k > 2, intersection number c2 > 2 and an eigenvalue θ satisfying −k < θ 6 2 − k. Moreover, we give a lower bound for valency k which implies θD > 2− k for distance-regular graphs with girth g > 5 satisfying g = 5 or g ≡ 3 (mod 4).
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