Coloring of lattices

Nimbhokar, S. K.; Wasadikar, Meenakshi; Pawar, Madhukar M.

doi:10.2478/s12175-010-0022-x

Cited by 18 publications

(16 citation statements)

References 9 publications

(10 reference statements)

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“…Thus a similar question can be asked for commutative semigroups with 0, see [9]. In a recent paper [10] Nimbhokar, Wasadikar and Demeyer have shown that Beck's conjecture holds for the class of ∧-semilattices with 0, i.e., commutative and idempotent semigroups with 0, see [4] and [7].…”

mentioning

confidence: 93%

The Zerodivisor Graph of a Qoset

Halaš

Länger

2009

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confidence: 93%

The Zerodivisor Graph of a Qoset

Halaš

Länger

2009

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“…Nimbhorkar, Wasadikar and Pawar in [9] have associated a graph with a lattice L with 0 by saying that two elements are adjacent if and only if their meet is 0. Similarly we can define a graph with a lattice L with 0 by saying that two nonzero elements a, b ∈ L are adjacent if and only if a ∧ b = 0 and call this graph as the zero divisor graph of L and denote it by Γ (L).…”

Section: Definition 2 a Connected Acyclic Graph Is Called A Treementioning

confidence: 99%

“…The papers of Gadenova [5], Bollobas and Rival [1] discuss the properties of covering graphs derived from lattices. In [9] Nimbhorkar, Wasadikar and Pawar defined graphs on a lattice L with 0, by defining adjacency of two elements x, y ∈ L by x ∧ y = 0.…”

Section: Introductionmentioning

confidence: 99%

Incomparability Graphs of Lattices

Wasadikar

Survase

2012

Mathematical Modelling and Scientific Computation

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Abstract. Let L be a finite lattice with atleast two atoms and W (L) = {x | there exists y ∈ L such that x y }. The incomparability graph of L, denoted by Γ (L), is a graph with vertex set W (L) and two distinct vertices a, b ∈ W (L) are adjacent if and only if they are incomparable. In this paper, we study the incomparability graphs of lattices. We prove that, a disconnected graph is a graph of a lattice L if and only if L is of the form L1 L2. We prove that, Γ (L) cannot be an n-gon for any n ≥ 5. Some properties of incomparability graphs are obtained.

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“…Nimbhorkar, Wasadikar and Pawar [10] associated a zero-divisor graph to a lattice L with 0, whose vertices are the elements of L and two distinct elements are adjacent if and only if their meet is 0. Similarly in [11] we define a graph of a lattice L with 0.…”

Section: Some Realizable and Non Realizable Graphsmentioning

confidence: 99%

“…The papers of Gadenova [6], Bollobas and Rival [2] discuss the properties of covering graphs derived from lattices. Nimbhorkar, Wasadikar and Pawar [10] defined the zero-divisor graphs of a lattice L with 0, by defining the adjacency of two elements x, y ∈ L by x ∧ y = 0.…”

Section: Introductionmentioning

confidence: 99%

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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Coloring of lattices

Cited by 18 publications

References 9 publications

The Zerodivisor Graph of a Qoset

The Zerodivisor Graph of a Qoset

Incomparability Graphs of Lattices

Incomparability Graphs of Lattices II

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