Decomposing certain equipartite graphs into sunlet graphs of length \(2p\). (English) Zbl 1354.05111
Summary: For any integer \(r\geq3\), we define the sunlet graph of order \(2r\), denoted \(L_{2r}\), as the graph consisting of a cycle of length \(r\) together with \(r\) pendant vertices, each adjacent to exactly one vertex of the cycle. In this paper, we give necessary and sufficient conditions for decomposing the lexicographic product of the complete graph and the complete graph minus a 1-factor, with complement of the complete graph \(K_m\), (that is \(K_n\otimes\bar{K}_m\) and \(K_n-I\otimes\bar{K}_m\), respectively) into sunlet graphs of order twice a prime.
MSC:
| 05C70 | Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) |
| 05C76 | Graph operations (line graphs, products, etc.) |
| 05C12 | Distance in graphs |
| 05C38 | Paths and cycles |
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