TY - JOUR
T1 - An inequality involving the second largest and smallest eigenvalue of a distance-regular graph
AU - Koolen, Jack H.
AU - Park, Jongyook
AU - Yu, Hyonju
PY - 2011/6/15
Y1 - 2011/6/15
N2 - For a distance-regular graph with second largest eigenvalue (resp., smallest eigenvalue) θ1 (resp., θD) we show that (θ1+1)(θD+1)≤-b1 holds, where equality only holds when the diameter equals two. Using this inequality we study distance-regular graphs with fixed second largest eigenvalue.
AB - For a distance-regular graph with second largest eigenvalue (resp., smallest eigenvalue) θ1 (resp., θD) we show that (θ1+1)(θD+1)≤-b1 holds, where equality only holds when the diameter equals two. Using this inequality we study distance-regular graphs with fixed second largest eigenvalue.
KW - Bounds on eigenvalues
KW - Distance-regular graph
KW - Shill distance-regular graphs
KW - Tight distance-regular graph
UR - http://www.scopus.com/inward/record.url?scp=79952628984&partnerID=8YFLogxK
U2 - 10.1016/j.laa.2010.12.032
DO - 10.1016/j.laa.2010.12.032
M3 - Article
AN - SCOPUS:79952628984
SN - 0024-3795
VL - 434
SP - 2404
EP - 2412
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
IS - 12
ER -