Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ENUMERATION OF OPTIMALLY LABELLED GRAPHS OF BANDWIDTH 2

  • Chae, Gab-Byung (Division of Mathematics and Informational Statistics Wonkwang University) ;
  • Cheong, MinSeok (College of Informatics, Information Security Convergence Korea University) ;
  • Kim, Sang-Mok (Department of Mathematics Kwangwoon University)
  • Received : 2016.02.25
  • Accepted : 2017.08.17
  • Published : 2017.11.30
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Abstract

An optimally labelled graph of bandwidth 2 is an ordered pair (G, f) where G is a simple graph with bw(G) = 2 and $f:V(G){\rightarrow}[n]$ is a bijection such that bw(G, f) = 2. In this paper, the number of optimally labelled graphs of bandwidth two of order n is enumerated by counting linear forests.

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References

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  2. G.-B. Chae, M. Cheong, and S.-M. Kim, Irreducible posets of linear discrepancy 1 and 2, Far East J. Math. Sci. (JMS) 22 (2006), no. 2, 217-226.
  3. G.-B. Chae, Graph bandwidth with irreducibility, Preprint.