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

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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 -