Orthogonal Systems in Finite Graphs

Abstract

Given a finite graph G there is a corresponding group given by the presentation with generators the vertices of G and a relation [x,y]=1 for generators x and y precisely when (x,y) is an edge of G. Such groups are known as partially commutative groups (or right-angled Artin groups). In this paper we construct orthogonality theory for graphs with the study of partially commutative groups in mind. The theory developed here provides tools for the study of the structure of the centraliser lattice of partially commutative groups and for their automorphism groups.