Abstract
Let \(P_{k}\) and \(C_k\) respectively denote a path and a cycle on \(k\) vertices. In this paper we give necessary and sufficient conditions for the existence of \(\{P_{5}, C_4\}_{\{p, q\}}\)-decomposition of tensor product and cartesian product of complete graphs. Further we extent such decomposition to complete multipartite graphs.
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Acknowledgments
The authors are grateful to the anonymous referees for their valuable suggestions and comments, which improved the presentation of the paper. The first author thanks the University Grants Commission for its support (Grant No.F.4-7/2008(BSR)/11-105/2008(BSR)/ December 2012). The second author thank the Department of Science and Technology, Government of India, New Delhi for its financial support through the Grant No. DST/ SR/ S4/ MS:282/13.
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Jeevadoss, S., Muthusamy, A. Decomposition of Product Graphs into Paths and Cycles of Length Four. Graphs and Combinatorics 32, 199–223 (2016). https://doi.org/10.1007/s00373-015-1564-z
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DOI: https://doi.org/10.1007/s00373-015-1564-z