Title : ( Planar zero divisor graphs of partially ordered sets )
Authors: M. Afkhami , Zahra Barati , Kazem Khashyarmanesh ,
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Abstract
In this paper, we associated a graph G^*(P) to a partially ordered set (poset, briefly) with the least element 0, as an undirected graph with vertex set P^*= P\setminus {0} and, for two distinct vertices x and y, x is adjacent to y in G^*(P) if and only if \{x,y\}^\ell={0}, where, for a subset S of P, S^l is the set of all elements x\in P with x\leq s for all s\in S. We study some basic properties of G^*(P). Also, we completely investigate the planarity of G^*(P).
Keywords
, partially ordered set, planar graph, Zero divisor graph
@article{paperid:1033830,
author = {M. Afkhami and Barati, Zahra and Khashyarmanesh, Kazem},
title = {Planar zero divisor graphs of partially ordered sets},
journal = {Acta Mathematica Hungarica},
year = {2012},
volume = {137},
number = {1},
month = {January},
issn = {0236-5294},
pages = {27--35},
numpages = {8},
keywords = {partially ordered set; planar graph; Zero divisor graph},
}
%0 Journal Article
%T Planar zero divisor graphs of partially ordered sets
%A M. Afkhami
%A Barati, Zahra
%A Khashyarmanesh, Kazem
%J Acta Mathematica Hungarica
%@ 0236-5294
%D 2012
