## $$N$$-sun decomposition of complete, complete bipartite and some Harary graphs.(English)Zbl 1186.05094

Summary: Graph decompositions are vital in the study of combinatorial design theory. A decomposition of a graph $$G$$ is a partition of its edge set. An $$n$$-sun graph is a cycle $$C_n$$ with an edge terminating in a vertex of degree one attached to each vertex. In this paper, we define $$n$$-sun decomposition of some even order graphs with a perfect matching. We have proved that the complete graph $$K_{2n}$$, complete bipartite graph $$K_{2n,2n}$$ and the Harary graph $$H_{4,2n}$$ have $$n$$-sun decompositions. A labeling scheme is used to construct the $$n$$-suns.

### MSC:

 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)

### Keywords:

decomposition; Hamilton cycle; perfect matching; spanning tree
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