Abstract
A graph G is a prime distance graph if its vertices can be labeled with distinct integers such that for any two adjacent vertices, the difference of their labels is a prime number. It is known that cycles and bipartite graphs are prime distance graphs. In this paper we derive some general results concerning prime distance labeling of graphs and also establish interesting results for complete graphs, wheel graphs, and wheel-related graphs.
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Acknowledgements
The authors are very much grateful for the valuable and detailed comments of the reviewer, especially in providing elegant and simplified forms of proofs of certain results. The comments have served to be very useful in improving the presentation of the paper. The first author Dr.A. Parthiban wishes to thank his wife, Mrs. Steffy Princy Parthiban for her constant help and encouragement in completing this research work.
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Communicated by Gadadhar Misra.
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Parthiban, A., Samdanielthompson, G. & Kumar, K.S. ON FINITE PRIME DISTANCE GRAPHS. Indian J Pure Appl Math 52, 22–26 (2021). https://doi.org/10.1007/s13226-021-00135-3
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DOI: https://doi.org/10.1007/s13226-021-00135-3