With any symmetrizable integer Cartan matrix C∈ SC arn⊆ M n (Z), a Z-invertible Coxeter
matrix Cox C∈ M n (Z) is associated. We study such positive definite matrices up to a strong …

We continue the Coxeter spectral study of the category 𝒰ℬigr m of loop-free edge-bipartite
(signed) graphs Δ, with m≥ 2 vertices, we started in [SIAM J. Discr. Math. 27 (2013), 827 …

In this two parts article with the same title we continue the Coxeter spectral study of the
category 𝒰ℬigr m of loop-free edge-bipartite (signed) graphs Δ, with m≥ 2 vertices, we …

By applying an advanced technique of Weyl orbits of matrix morsifications of Dynkin graphs
we obtain a complete classification (up to the strong Gram Z-congruence) of the connected …

We develop a computational technique for classification of a class of signed graphs (called
edge-bipartite graphs), we started in Simson (2013)[42] and Bocian et al.(2014)[6]. Here we …

We study edge-bipartite graphs (bigraphs), a class of signed graphs, by means of the
inflation algorithm which relies on performing certain elementary transformations on a given …

We continue the study of finite connected edge-bipartite graphs Δ, with m≥ 2 vertices (a
class of signed graphs), started in [SIAM J. Discrete Math. 27 (2013), 827-854] and …

We continue the study of finite connected loop-free edge-bipartite graphs Δ, with m≥ 3
vertices (a class of signed graphs), we started in Simson (2013)[48] and M. Gąsiorek et …

Cartan matrices and quasi-Cartan matrices play an important role in such areas as Lie
theory, representation theory, and algebraic graph theory. It is known that each (connected) …

Following a Coxeter spectral analysis problems for positive edge-bipartite graphs (signed
multigraphs with a separation property) introduced in [SIAM J. Discr. Math. 27 (2013), 827 …