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 CoxΔ, the Coxeter spectrum speccΔ, 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 GΔ and GDΔ. We also present a toroidal mesh algorithm that allows us to construct a Z-congruence of the non-symmetric Gram matrices and , if the Coxeter spectra speccΔ and speccΔ′ coincide.