Distance-regular graphs with an eigenvalue -k < theta <= 2-k

Title
Distance-regular graphs with an eigenvalue -k < theta <= 2-k
Author(s)
방세정
Issue Date
201401
Publisher
ELECTRONIC JOURNAL OF COMBINATORICS
Citation
ELECTRONIC JOURNAL OF COMBINATORICS, v.21, no.1
Abstract
It is known that bipartite distance-regular graphs with diameter D >= 3, valency k >= 3, intersection number c(2) >= 2 and eigenvalues k = theta(0) > theta(1) > ... > theta(D) satisfy theta(1) <= k-2 and thus theta(D-1) >= 2-k. In this paper we classify non-complete distanceregular graphs with valency k 2, intersection numberc(2) >= 2 and an eigenvalue -k satisfying -k < theta <= 2-k. Moreover, we give a lower bound for valency k which implies OD 2 k for distance-regular graphs with girth g >= 5 satisfying g = 5 or g 3 (mod 4).
URI
http://hdl.handle.net/YU.REPOSITORY/33523
ISSN
1077-8926
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이과대학 > 수학과 > Articles
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