Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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DISTANCE TWO LABELING ON THE SQUARE OF A CYCLE

  • ZHANG, XIAOLING (College of Mathematics and Computer Science Quanzhou Normal University)
  • Received : 2015.09.02
  • Accepted : 2015.11.30
  • Published : 2015.12.30
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Abstract

An L(2; 1)-labeling of a graph G is a function f from the vertex set V (G) to the set of all non-negative integers such that ${\mid}f(u)-f(v){\mid}{\geq}2$ if d(u, v) = 1 and ${\mid}f(u)-f(v){\mid}{\geq}1$ if d(u, v) = 2. The ${\lambda}$-number of G, denoted ${\lambda}(G)$, is the smallest number k such that G admits an L(2, 1)-labeling with $k=\max\{f(u){\mid}u{\in}V(G)\}$. In this paper, we consider the square of a cycle and provide exact value for its ${\lambda}$-number. In addition, we also completely determine its edge span.

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References

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