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ON FINITE PRIME DISTANCE GRAPHS

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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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Authors and Affiliations

  1. Department of Mathematics, Lovely Professional University, Punjab, 144 411, India

    A. Parthiban

  2. Department of Mathematics, Hindustan College of Arts and Science, Chennai, 603 103, India

    G. Samdanielthompson

  3. Department of Mathematics, Madras Christian College, Chennai, 600 059, India

    K. Sathish Kumar

Authors
  1. A. Parthiban
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  2. G. Samdanielthompson
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  3. K. Sathish Kumar
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Corresponding author

Correspondence to A. Parthiban.

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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

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