On the existence of k-sun systems

A k-sun graph S(Ck) is obtained from the cycle of length k, Ck, by adding a pendant edge to each vertex of Ck. A k-sun system of order v is a decomposition of the complete graph Kv into k-sun graphs. In this paper, we use a difference method to obtain k-sun systems of all possible orders for k=6,10,...

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Bibliographic Details
Published inDiscrete mathematics Vol. 312; no. 12-13; pp. 1931 - 1939
Main Authors Fu, C.-M., Jhuang, N.-H., Lin, Y.-L., Sung, H.-M.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 06.07.2012
Subjects
[formula omitted]-sun graph
Complete graph
Crown graph
Cycle system
Decomposition
Graph decomposition
Graph design
Graph decomposition
Complete graph
Crown graph
k-sun graph
Decomposition
Graph design
Cycle system
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Summary:A k-sun graph S(Ck) is obtained from the cycle of length k, Ck, by adding a pendant edge to each vertex of Ck. A k-sun system of order v is a decomposition of the complete graph Kv into k-sun graphs. In this paper, we use a difference method to obtain k-sun systems of all possible orders for k=6,10,14 and 2t where t is a positive integer at least 2. More precisely, we obtain cyclic k-sun systems of odd order and 1-rotational k-sun systems of even order when the order is greater than 4k.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2012.03.007