TY - JOUR
T1 - 2-Walk-regular graphs with a small number of vertices compared to the valency
AU - Qiao, Zhi
AU - Koolen, Jack H.
AU - Park, Jongyook
N1 - Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - In 2013, it was shown that, for a given real number α>2, there are only finitely many distance-regular graphs Γ with valency k and diameter D≥3 having at most αk vertices, except for the following two cases: (i) D=3 and Γ is imprimitive; (ii) D=4 and Γ is antipodal and bipartite. In this paper, we will generalize this result to 2-walk-regular graphs. In this case, also incidence graphs of certain group divisible designs appear.
AB - In 2013, it was shown that, for a given real number α>2, there are only finitely many distance-regular graphs Γ with valency k and diameter D≥3 having at most αk vertices, except for the following two cases: (i) D=3 and Γ is imprimitive; (ii) D=4 and Γ is antipodal and bipartite. In this paper, we will generalize this result to 2-walk-regular graphs. In this case, also incidence graphs of certain group divisible designs appear.
KW - Distance-regular graphs
KW - Dual property
KW - Group divisible designs
KW - t-walk-regular graphs
UR - http://www.scopus.com/inward/record.url?scp=84982126104&partnerID=8YFLogxK
U2 - 10.1016/j.laa.2016.07.027
DO - 10.1016/j.laa.2016.07.027
M3 - Article
AN - SCOPUS:84982126104
SN - 0024-3795
VL - 510
SP - 10
EP - 24
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -