A graph associated to a lattice |
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Authors: | Mojgan Afkhami Zahra Barati Kazem Khashyarmanesh |
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Institution: | 1. Department of Mathematics, University of Neyshabur, 91136-899, Neyshabur, Iran 2. Department of Pure Mathematics, Ferdowsi University of Mashhad, 1159-91775, Mashhad, Iran
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Abstract: | In this paper, we associate a simple graph to a lattice $\mathcal L $ , in which the vertex set is being the set of all elements of $\mathcal L $ , and two distinct vertices $x$ and $y$ are adjacent if $x\vee y\in S$ , when $S$ is a multiplicatively closed subset of $\mathcal L $ . We denote this graph by $\Gamma _S(\mathcal L )$ . We study some properties of $\Gamma _S(\mathcal L )$ . Moreover, we investigate the planarity of $\Gamma _S(\mathcal L )$ , whenever $S$ is a saturated multiplicatively closed subset of $\mathcal L $ . |
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