An inflation algorithm and a toroidal mesh algorithm for edge-bipartite graphs

We present algorithmic methods used in the spectral analysis of bigraphs Δ by means of the Coxeter matrix Cox Δ , the Coxeter spectrum specc Δ , and an inflation algorithm associating to any connected loop-free positive bigraph Δ a simply-laced Dynkin diagram DΔ, and defining a Z -congruence of the symmetric Gram matrices G Δ and G D Δ . We also present a toroidal mesh algorithm that allows us to construct a Z -congruence of the non-symmetric Gram matrices G ˇ Δ and G ˇ Δ ′ , if the Coxeter spectra specc Δ and specc Δ ′ coincide.