The zero divisor graphs of Boolean posets

Vinayak Joshi; Anagha Khiste

doi:10.2478/s12175-014-0221-y

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The zero divisor graphs of Boolean posets

Vinayak Joshi Anagha Khiste

Year: 2014 Journal: Mathematica Slovaca Vol: 64 (2)Pages: 511-519 Publisher: Springer Science+Business Media

DOI: 10.2478/s12175-014-0221-y

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Abstract

Abstract In this paper, it is proved that if B is a Boolean poset and S is a bounded pseudocomplemented poset such that S\Z(S) = {1}, then Γ(B) ≌ Γ(S) if and only if B ≌ S. Further, we characterize the graphs which can be realized as zero divisor graphs of Boolean posets.

Keywords:

Mathematics Combinatorics Partially ordered set Boolean algebras canonically defined Discrete mathematics Zero divisor Stone's representation theorem for Boolean algebras Zero (linguistics) Bounded function Divisor (algebraic geometry) Two-element Boolean algebra Algebra over a field Pure mathematics

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Rings, Modules, and Algebras

Physical Sciences → Mathematics → Algebra and Number Theory

Advanced Topics in Algebra

Physical Sciences → Mathematics → Algebra and Number Theory

Algebraic structures and combinatorial models

Physical Sciences → Mathematics → Geometry and Topology

The zero divisor graphs of Boolean posets

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