TY - JOUR
T1 - Distance-regular graphs with a 1 or c 2 at least half the valency
AU - Koolen, Jack H.
AU - Park, Jongyook
PY - 2012/4
Y1 - 2012/4
N2 - In this paper, we study the distance-regular graphs Γ that have a pair of distinct vertices, say x and y, such that the number of common neighbors of x and y is about half the valency of Γ. We show that if the diameter is at least three, then such a graph, besides a finite number of exceptions, is a Taylor graph, bipartite with diameter three or a line graph.
AB - In this paper, we study the distance-regular graphs Γ that have a pair of distinct vertices, say x and y, such that the number of common neighbors of x and y is about half the valency of Γ. We show that if the diameter is at least three, then such a graph, besides a finite number of exceptions, is a Taylor graph, bipartite with diameter three or a line graph.
KW - Distance-regular graphs
KW - Line graphs
KW - Taylor graphs
UR - http://www.scopus.com/inward/record.url?scp=81255164786&partnerID=8YFLogxK
U2 - 10.1016/j.jcta.2011.11.001
DO - 10.1016/j.jcta.2011.11.001
M3 - Article
AN - SCOPUS:81255164786
SN - 0097-3165
VL - 119
SP - 546
EP - 555
JO - Journal of Combinatorial Theory. Series A
JF - Journal of Combinatorial Theory. Series A
IS - 3
ER -