On distance two in Cayley graphs of Coxeter groups

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We consider the Cayley graph C(W,S) of a Coxeter system (W,S) and describe all maximal 2-cliques in this graph, i.e. maximal subsets in the vertex set such that the distance between any two distinct elements is equal to 2. As an application, we show that every automorphism of the half of Cayley graph is uniquely extendable to an automorphism of the Cayley graph if |S|≥ 5.