Incomparability Graphs of Lattices

Wasadikar, Meenakshi; Survase, Pradnya

doi:10.1007/978-3-642-28926-2_9

Cited by 7 publications

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References 5 publications

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“…Wasadikar and Survase [12] have shown that all connected graphs with at most four vertices can be realized as Γ (L).…”

Section: Some Realizable and Non Realizable Graphsmentioning

confidence: 99%

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Incomparability Graphs of Lattices II

Wasadikar¹,

Survase²

2012

Lecture Notes in Computer Science

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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 Kn with two horns is realizable as Γ (L). We also show that the complete graph K3 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.

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“…Wasadikar and Survase [12] have shown that all connected graphs with at most four vertices can be realized as Γ (L).…”

Section: Some Realizable and Non Realizable Graphsmentioning

confidence: 99%

“…Wasadikar and Survase [12] introduced the incomparability graph of a lattice. Throughout this paper, L is a finite lattice with at least two atoms.…”

Section: Introductionmentioning

confidence: 99%