TY - JOUR
T1 - Graph designs for the eight-edge five-vertex graphs
AU - Colbourn, Charles
AU - Ge, Gennian
AU - Ling, Alan C H
N1 - Funding Information:
Research for the first author was supported by the U.S. Army Research Office under grant DAAD19-01-1-0406. Research for the second author was supported by the National Outstanding Youth Science Foundation of China under Grant No. 10825103, National Natural Science Foundation of China under Grant No. 10771193, Zhejiang Provincial Natural Science Foundation of China, and Program for New Century Excellent Talents in University.
PY - 2009/11/28
Y1 - 2009/11/28
N2 - The existence of graph designs for the two nonisomorphic graphs on five vertices and eight edges is determined in the case of index one, with three possible exceptions in total. It is established that for the unique graph with vertex sequence (3, 3, 3, 3, 4), a graph design of order n exists exactly when n ≡ 0, 1 (mod 16) and n ≠ 16, with the possible exception of n = 48. For the unique graph with vertex sequence (2, 3, 3, 4, 4), a graph design of order n exists exactly when n ≡ 0, 1 (mod 16), with the possible exceptions of n ∈ {32, 48}.
AB - The existence of graph designs for the two nonisomorphic graphs on five vertices and eight edges is determined in the case of index one, with three possible exceptions in total. It is established that for the unique graph with vertex sequence (3, 3, 3, 3, 4), a graph design of order n exists exactly when n ≡ 0, 1 (mod 16) and n ≠ 16, with the possible exception of n = 48. For the unique graph with vertex sequence (2, 3, 3, 4, 4), a graph design of order n exists exactly when n ≡ 0, 1 (mod 16), with the possible exceptions of n ∈ {32, 48}.
KW - Decomposition
KW - G-designs
KW - G-designs
KW - Graph designs
UR - http://www.scopus.com/inward/record.url?scp=70350564449&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=70350564449&partnerID=8YFLogxK
U2 - 10.1016/j.disc.2008.10.015
DO - 10.1016/j.disc.2008.10.015
M3 - Article
AN - SCOPUS:70350564449
SN - 0012-365X
VL - 309
SP - 6440
EP - 6445
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 22
ER -