Geodesic
Orthogonal systems in finite graphs
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 151-176

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To a finite graph there corresponds a free partially commutative group: with the given graph as commutation graph. In this paper we construct an orthogonality theory for graphs and their corresponding free partially commutative groups. The theory developed here provides tools for the study of the structure of partially commutative groups, their universal theory and automorphism groups. In particular the theory is applied in this paper to the centraliser lattice of such groups. 
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     author = {A. J. Duncan and I. V. Kazachkov and V. N. Remeslennikov},
     title = {Orthogonal systems in finite graphs},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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     year = {2008},
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A. J. Duncan; I. V. Kazachkov; V. N. Remeslennikov. Orthogonal systems in finite graphs. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 151-176. http://geodesic.mathdoc.fr/item/SEMR_2008_5_a11/