Shahid Bahonar University of Kerman Journal of Mahani Mathematical Research 2251-7952 12 1 2023 01 01 The small intersection graph of filters of a bounded distributive lattice 311 326 3356 10.22103/jmmr.2022.19422.1248 EN Shahabaddin Ebrahimi Atani Department of Mathematics, University of Guilan, Rasht, Iran Mehdi Khoramdel Department of Mathematics, University of Guilan, Rasht, Iran Maryam Chenari Department of Mathematics, University of Guilan, Rasht, Iran Journal Article 2022 04 28 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. https://jmmrc.uk.ac.ir/article_3356_0943d92a92d13b9640fdb8b443fa4bdd.pdf