On the Intersection Graphs Associeted to Posets

Let ( ≤) be a poset with the least element 0. The intersection graph of ideals of , denoted by ), is a graph whose vertices are all nontrivial ideals of and two distinct vertices and are adjacent if and only if ∩ {0}. In this paper, we study the planarity and outerplanarity of the intersection graph...

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Published inDiscussiones mathematicae. General algebra and applications Vol. 40; no. 1; pp. 105 - 117
Main Authors Afkhami, M., Khashyarmanesh, K., Shahsavar, F.
Format Journal Article
LanguageEnglish
Published Sciendo 01.06.2020
University of Zielona Góra
Subjects
05C10
06A07
intersection graph
outerplanar graph
planar graph
poset
split graph
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Summary:Let ( ≤) be a poset with the least element 0. The intersection graph of ideals of , denoted by ), is a graph whose vertices are all nontrivial ideals of and two distinct vertices and are adjacent if and only if ∩ {0}. In this paper, we study the planarity and outerplanarity of the intersection graph ). Also, we determine all posets with split intersection graphs.
ISSN:1509-9415
2084-0373
DOI:10.7151/dmgaa.1322