Automorphism group of a graph constructed from a lattice

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.

Automorphism group of a graph constructed from a lattice Keywords:

Automorphism group of a graph , prime filter , automorphism group of a lattice , perfect maching of a graph