Abstract
A graph G is a prime distance graph if its vertices can be labeled with distinct integers in such a way that for any two adjacent vertices, the absolute 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 certain general results concerning prime distance labeling. We also investigate prime distance labeling of some cycle related graphs in the context of some graph operations, namely, power, fusion, duplication and vertex switching in cycle \(C_n\).
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Acknowledgement
The authors are very much grateful for the valuable and detailed comments of the reviewer. The comments have served to be very useful in correcting the errors and for improving the presentation of the paper. The first author A. Parthiban acknowledges with gratitude the award (No.: F1-17.1/2014-15/RGNF-2014-15-SC-TAM-65968/ (SA-III/Website)) of Rajiv Gandhi National Fellowship for SC students by UGC, India.
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Parthiban, A., David, N.G. (2017). On Prime Distance Labeling of Graphs. In: Arumugam, S., Bagga, J., Beineke, L., Panda, B. (eds) Theoretical Computer Science and Discrete Mathematics. ICTCSDM 2016. Lecture Notes in Computer Science(), vol 10398. Springer, Cham. https://doi.org/10.1007/978-3-319-64419-6_31
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DOI: https://doi.org/10.1007/978-3-319-64419-6_31
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