Discrete Mathematics, Algorithms and Applications, Volume (6), No (3), Year (2014-3) , Pages (14500360-14500369)

Title : ( The intersection graph of ideals of a poset )

Authors: Mojgan Afkhami , Kazem Khashyarmanesh ,

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Let (P,≤) be a partially ordered set (poset, briefly) with a least element 0. The intersection graph of ideal of P, denoted by G(P), is a graph whose vertices are all non-trivial ideals of P and two distinct vertices I and J are adjacent if and only if I ∩ J \not= {0}. In this paper, we study some relations between the algebraic properties of posets and graph-theoretic properties of G(P). We investigate the connectivity, diameter, girth and planarity of the intersection graph. Also, among the other things, we show that if the clique number of G(P) is finite, then P is finite too.


Partially ordered set; intersection graph; clique number.
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author = {Mojgan Afkhami and Khashyarmanesh, Kazem},
title = {The intersection graph of ideals of a poset},
journal = {Discrete Mathematics, Algorithms and Applications},
year = {2014},
volume = {6},
number = {3},
month = {March},
issn = {1793-8309},
pages = {14500360--14500369},
numpages = {9},
keywords = {Partially ordered set; intersection graph; clique number.},


%0 Journal Article
%T The intersection graph of ideals of a poset
%A Mojgan Afkhami
%A Khashyarmanesh, Kazem
%J Discrete Mathematics, Algorithms and Applications
%@ 1793-8309
%D 2014