\(L(2,1)\)-Labeling of Cartesian Product of Complete Bipartite Graph and Path

Authors

  • Sumonta Ghosh 1Department of Mathematics, NIT Durgapur, Durgapur, West Bengal 713209
  • Satyabrata Paul Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, West Bengal 721102
  • Anita Pal Department of Mathematics, NIT Durgapur, Durgapur, West Bengal 713209

DOI:

https://doi.org/10.26713/jims.v9i3.817

Keywords:

\(L(2, 1)\)-labeling, Graph labeling, Cartesian product of graphs

Abstract

An \(L(2,1)\)-labeling problem is a particular case of \(L(h,k)\)-labeling problem. An \(L(2,1)\)-labeling of a graph \(G=(V,E)\) is a function \(f\) from the set of vertices \(V\) to the set of positive integers. For any two vertices \(x\) and \(y\), the label difference \(|f(x)-f(y)|\geq2\) when \(d(x,y)=1\) and \(|f(x)-f(y)|\geq1\) when \(d(x,y)=2\) where \(d(x,y)\) is the distance between the vertices \(x\) and \(y\). In this paper we label the graph which is obtained by Cartesian product between complete bipartite graph and path by \(L(2,1)\)-labeling. We provide upper bound of the label in terms of number of vertices and edges. The bound is linear with respect to the order and size of the graph. This is a very good bound compare to the bound of Griggs and Yeh Conjecture.

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Published

2017-10-31
CITATION

How to Cite

Ghosh, S., Paul, S., & Pal, A. (2017). \(L(2,1)\)-Labeling of Cartesian Product of Complete Bipartite Graph and Path. Journal of Informatics and Mathematical Sciences, 9(3), 685–698. https://doi.org/10.26713/jims.v9i3.817

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Research Articles