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L(0,1)-labelling of Permutation Graphs

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Journal of Mathematical Modelling and Algorithms in Operations Research

Abstract

L(0,1)-labelling of a graph G=(V,E) is a function f from the vertex set V(G) to the set of non-negative integers such that adjacent vertices get number zero apart, and vertices at distance two get distinct numbers. The goal of L(0,1)-labelling problem is to produce a legal labelling that minimize the largest label used. In this article, it is shown that, for a permutation graph G with maximum vertex degree Δ, the upper bound of λ 0,1(G) is Δ−1. Finally, we prove that the result is exact for bipartite permutation graph.

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Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer, Programming, Vidyasagar University, Midnapore, 721102, India

    Satyabrata Paul & Madhumangal Pal

  2. Department of Mathematics, National Institute of Technology Durgapur, Durgapur, 713209, India

    Anita Pal

Authors
  1. Satyabrata Paul
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  2. Madhumangal Pal
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  3. Anita Pal
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Correspondence to Satyabrata Paul.

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Paul, S., Pal, M. & Pal, A. L(0,1)-labelling of Permutation Graphs. J Math Model Algor 14, 469–479 (2015). https://doi.org/10.1007/s10852-015-9280-5

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  • DOI: https://doi.org/10.1007/s10852-015-9280-5

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