Graph designs for the eight-edge five-vertex graphs

Charles Colbourn; Gennian Ge; Alan C H Ling

doi:10.1016/j.disc.2008.10.015

Graph designs for the eight-edge five-vertex graphs

Charles Colbourn, Gennian Ge, Alan C H Ling

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

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}.

Original language	English (US)
Pages (from-to)	6440-6445
Number of pages	6
Journal	Discrete Mathematics
Volume	309
Issue number	22
DOIs	https://doi.org/10.1016/j.disc.2008.10.015
State	Published - Nov 28 2009

Keywords

Decomposition
G-designs
G-designs
Graph designs

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2008.10.015

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title = "Graph designs for the eight-edge five-vertex graphs",

abstract = "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}.",

keywords = "Decomposition, G-designs, G-designs, Graph designs",

author = "Charles Colbourn and Gennian Ge and Ling, {Alan C H}",

note = "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.",

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doi = "10.1016/j.disc.2008.10.015",

language = "English (US)",

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journal = "Discrete Mathematics",

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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 - Graph designs

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Graph designs for the eight-edge five-vertex graphs

Abstract

Keywords

ASJC Scopus subject areas

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