Geodesic
Decomposition of complete graphs into $(0,2)$-prisms
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 37-43 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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R. Frucht and J. Gallian (1988) 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 $\rho ^{+}$-labeling introduced by S. I. El-Zanati, C. Vanden Eynden, and N. Punnim (2001) 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 $x$.
R. Frucht and J. Gallian (1988) 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 $\rho ^{+}$-labeling introduced by S. I. El-Zanati, C. Vanden Eynden, and N. Punnim (2001) 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 $x$.
DOI : 10.1007/s10587-014-0080-2
Classification : 05B30, 05C51, 05C70, 05C78
Keywords: decompositions; prism; $\rho ^+$-labeling 
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Cichacz, Sylwia; Dib, Soleh; Froncek, Dalibor. Decomposition of complete graphs into $(0,2)$-prisms. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 37-43. doi: 10.1007/s10587-014-0080-2

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