Authors: P. Paulraja, R. Srimathi Title: Decomposition of the tensor product of graphs into cycles of lengths 3 and 6 Source: Discussiones Mathematicae Graph Theory Received 03.03.2018, Revised 03.10.2018, Accepted 03.10.2018, doi: 10.7151/dmgt.2178 | |
Abstract: By a \big{C_{3}^{&}alpha;,C_{6}^{&}beta;\big}-decomposition of a graph G, we mean a partition of the edge set of G into α cycles of length 3 and β cycles of length 6. In this paper, necessary and sufficient conditions for the existence of a \big{C_{3}^{&}alpha;,C_{6}^{&}beta;\big}-decomposition of (K_{m}× K_{n})(λ), where × denotes the tensor product of graphs and λ is the multiplicity of the edges, is obtained. In fact, we prove that for λ≥ 1, m,n≥ 3 and (m,n)≠(3,3), a \big{C_{3}^{&}alpha;,C_{6}^{&}beta;\big}-decomposition of (K_{m}× K_{n})(λ) exists if and only if λ(m-1)(n-1)≡ 0 (mod 2) and 3α+6β=\frac{λ m(m-1)n(n-1)}{2}. | |
Keywords: cycle decomposition, tensor product | |
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