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 …

In this two parts article with the same main title we study a problem of Coxeter-Gram spectral
analysis of edge-bipartite graphs (bigraphs), a class of signed graphs. We ask for a criterion …

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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 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 …

Cartan matrices, quasi-Cartan matrices and associated integral quadratic forms and root
systems play an important role in such areas like Lie theory, representation theory and …

We continue the Coxeter spectral study of finite positive edge-bipartite signed (multi) graphs
Δ (bigraphs, for short), with n≥ 2 vertices started in Simson (2013)[44] and developed in …