The small intersection graph of filters of a bounded distributive lattice

Document Type : Research Paper

Authors

Department of Mathematics, University of Guilan, Rasht, Iran

Abstract

Let $L$ be a lattice with $1$ and $0$. The small intersection graph of filters of $L$, denoted by $\Gamma(L)$, is defined to be a graph whose vertices are in one to one correspondence with all non-trivial filters of $L$ and two distinct vertices are adjacent if and only if the intersection of corresponding filters of $L$ is a small filter of $L$. In this paper, the basic  properties and possible structures of the graph $\Gamma(L)$ are investigated. Moreover, the complemented property, the domination number and the planar property of $\Gamma(L)$ are considered.

Keywords

References

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Journal of Mahani Mathematical Research
Volume 12, Issue 1 - Serial Number 24
January 2023
Pages 311-326

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History

  • Receive Date: 28 April 2022
  • Revise Date: 11 July 2022
  • Accept Date: 29 July 2022

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