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 Γ(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 Γ(L) are investigated. Moreover, the complemented property, the domination number and the planar property of Γ(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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