On Permutation Labeling of Graphs


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Authors

  • Mitesh J. Patel Department of Mathematics, Tolani College of Arts abd Science, Adipur-Kachchh, Gujarat, India
  • G. V. Ghodasara Department of Mathematics, H. & H. B. Kotak Institute of Science, Rajkot, Gujarat,India

Keywords:

Permutation labeling, Wheel graph, Bistar graph, Arbitrary super subdivision

Abstract

An injective function $f:V(G)\rightarrow{}\{1,2,\ldots,|V(G)|\}$ is said to be permutation labeling if each edge $uv$ is assigned with label $\Perm{f(u)}{f(v)}= \ \frac{(f(u))!}{| f(u)-f(v)|! } \ (f(u)>f(v))$ are all distinct. A graph which admits permutation labeling is called permutation graph. In this paper we prove that wheel graph, restricted square and degree splitting graph of bistar graph are permutation graphs. We also proved that arbitrary super subdivision of path graph, star graph and cycle graph are permutation graphs.

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Published

15-03-2021

How to Cite

Mitesh J. Patel, & G. V. Ghodasara. (2021). On Permutation Labeling of Graphs. International Journal of Mathematics And Its Applications, 9(1), 27–33. Retrieved from https://ijmaa.in/index.php/ijmaa/article/view/98

Issue

Vol. 9 No. 1 (2021)

Section

Research Article

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.