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Decomposition of complete graphs into \((0,2)\)-prisms. (English) Zbl 1340.05185
Summary: R. W. Frucht and J. A. Gallian [Ars Comb. 26, 69–82 (1988; Zbl 0678.05053)] proved that bipartite prisms of order \(2n\) have an \(\alpha \)-labeling, thus they decompose the complete graph \(K_{6nx+1}\) for any positive integer \(x\). We use a technique called the \(\varrho ^{+}\)-labeling introduced by S. I. El-Zanati et al. [Australas. J. Comb. 24, 209–219 (2001; Zbl 0983.05063)] to show that also some other families of 3-regular bipartite graphs of order \(2n\) called generalized prisms decompose the complete graph \(K_{6nx+1}\) for any positive integer \(x\).
MSC:
05C51 Graph designs and isomorphic decomposition
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C78 Graph labelling (graceful graphs, bandwidth, etc.)
05B30 Other designs, configurations
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