ðə kˈɑːksɛɾɚ ɡɹˈæf ɪz ˈɔːlsoʊ juːnˈiːkli dɪtˈɜːmɪnd baɪ ɪts ɡɹˈæf spˈɛktɹəm, ðə sˈɛt ʌv ɡɹˈæf ˈaɪdʒənvˌæljuːz ʌv ɪts ɐdʒˈeɪsənsi mˈeɪtɹɪks.
The Coxeter graph is also uniquely determined by its graph spectrum, the set of graph eigenvalues of its adjacency matrix.