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Decomposition of Cartesian product of complete graphs into paths and stars with four edges

Arockiajeyaraj P. Ezhilarasi; Appu Muthusamy — 2021

Commentationes Mathematicae Universitatis Carolinae

Let $P_{k}$ and $S_{k}$ denote a path and a star, respectively, on $k$ vertices. We give necessary and sufficient conditions for the existence of a complete ${P_{5}, S_{5}}$ -decomposition of Cartesian product of complete graphs.

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