Abstract
A graph G(p,q) is said to be modular multiplicative divisor (MMD) if there exist a one-to-one and on to function f from vertices of the graph to set of all natural numbers from 1 to p and label induced on the edges defined by the product of labels of end vertices modulo p such that addition of all edge labels is congruent to 0 (mod p).This paper studies the construction of larger families of graphs resulting from one of the graph operations namely even arbitrary super subdivision and the roll of MMD labeling in the context of Cartesian product of two graphs. Finally we discussed the open problem which is related to the application of MMD labeling in the absence of some parameters.
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References
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Acknowledgements
I would like to thank my supervisor Dr. S. Ganesh Professor, Department of Mathematics, Sathyabama Institute of Science and Technology for his continuous support and encouragement. Also I would like to thank my co-authors for their contribution towards the completion of the manuscript.
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RR performed the computations and verified the graph labeling condition. RR wrote the manuscript in consultation with DA and IA. All authors discussed the results and contributed to the final manuscript. All authors provided critical feedback and helped shape the research, analysis and manuscript.
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Does there exists MMD labeling for arbitrary supersubdivision of Cartesian product of any two connected graphs?
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Revathi, R., Angel, D. & Annammal, I. MMD labeling of EASS of cartesian product of two graphs. OPSEARCH 60, 870–876 (2023). https://doi.org/10.1007/s12597-023-00637-0
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DOI: https://doi.org/10.1007/s12597-023-00637-0