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On Prime Distance Labeling of Graphs

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Theoretical Computer Science and Discrete Mathematics (ICTCSDM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10398))

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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Authors and Affiliations

  1. Department of Mathematics, Madras Christian College, Chennai, 600059, Tamil Nadu, India

    A. Parthiban & N. Gnanamalar David

Authors
  1. A. Parthiban
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  2. N. Gnanamalar David
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Corresponding author

Correspondence to A. Parthiban .

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Editors and Affiliations

  1. Kalasalingam University, Krishnankoil, India

    S. Arumugam

  2. Ball State University, Muncie, Indiana, USA

    Jay Bagga

  3. Indiana University – Purdue University, Fort Wayne, Indiana, USA

    Lowell W. Beineke

  4. Indian Institute of Technology, New Delhi, India

    B.S. Panda

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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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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-64418-9

  • Online ISBN: 978-3-319-64419-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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