Authors : Imran R.; Ilayaraja M.; Bhuvaneswari R.; Abiramasundari C.

Volume/Issue : Volume 11 - 2026, Issue 5 - May

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Google Scholar : https://tinyurl.com/yj8ac7nv

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DOI : https://doi.org/10.38124/ijisrt/26May1812

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Abstract : This paper establishes necessary and sufficient conditions for the existence of decompositions of complete bipartite graphs into cycles and stars in certain classes of cases. Explicit constructions are provided for all admissible parameter sets. In addition, a Python implementation is developed to verify the theoretical conditions and to generate corresponding decompositions.

References :

1. Alspach, B., Gavlas, H. (2001). Cycle decompositions of Kn and Kn-I. Journal of Combinatorial Theory, Series B, 81(1), 77–99.
2. Bondy, J. A., Murty, U. R. S. (1976). Graph Theory with Applications. Macmillan Press, New York.
3. Jeevadoss, S., Muthusamy, A. (2014). Decomposition of complete bipartite graphs into paths and cycles. Discrete Mathematics, 331, 98–108.
4. M. Ilayaraja and A. Muthusamy. Decomposition of Complete Graphs. Indian Journal of Discrete Mathematics, 4 (2018), 13–33.
5. M. Ilayaraja and A. Muthusamy. Decomposition of Complete Bipartite Graphs into Cycles and Stars with Four Edges. AKCE International Journal of Graphs and Combinatorics, 17 (2020), 697–702.