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Incomparability Graphs of Lattices II

  • Meenakshi Wasadikar
  • Pradnya Survase
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7643)

Abstract

In this paper, we study some graphs which are realizable and some which are not realizable as the incomparability graph (denoted by Γ′(L)) of a lattice L with at least two atoms. We prove that for n ≥ 4, the complete graph K n with two horns is realizable as Γ′(L). We also show that the complete graph K 3 with three horns emanating from each of the three vertices is not realizable as Γ′(L), however it is realizable as the zero-divisor graph of L. Also we give a necessary and sufficient condition for a complete bipartite graph with two horns to be realizable as Γ′(L) for some lattice L.

Keywords

Incomparability graph bipartite graph horn double star graph zero-divisor graph 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Meenakshi Wasadikar
    • 1
  • Pradnya Survase
    • 1
  1. 1.Department of MathematicsDr. B.A.M. UniversityAurangabadIndia

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