Automorphism group of a graph constructed from a lattice

Document Type : Full Length Article

Authors

1 Department of Mathematics

2 Department of Mathematics, University of Kashan

Abstract

Let $L$ 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.

Graphical Abstract

Automorphism group of a graph constructed from a lattice

Keywords

Main Subjects


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