Shahid Rajaee Teacher Training UniversityJournal of Discrete Mathematics and Its Applications2981-08099320240901Automorphism group of a graph constructed from a lattice173179218310.22061/jdma.2024.11157.1082ENShahide MalekpourDepartment of MathematicsBehnam BazigaranDepartment of Mathematics, University of KashanJournal Article20240811Let $L$ be a lattice and $S$ be a $\wedge$-closed subset of $L$. The graph $\Gamma_{S}(L)$ is a simple graph with all elements of $L$ as vertex set and two distinct vertex $x,y$ are adjacent if and only if $x\vee y\in S$. In this paper, we verify the automorphism group of $\Gamma_{S}(L)$ and the relation by automorphism group of the lattice $L$. Also we study some properties of the graph $\Gamma_{S}(L)$ where $S$ is a prime filter or an ideal such as the perfect maching.https://jdma.sru.ac.ir/article_2183_94459280bc24c4573d2e828fbd8ad4ca.pdf