Inflation algorithm for loop-free non-negative edge-bipartite graphs of corank at least two

DOI10.1016/j.laa.2017.02.021zbMath1361.05061OpenAlexW2592427223MaRDI QIDQ526287

Daniel Simson, Katarzyna Zając

Publication date: 10 May 2017

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2017.02.021

zbMATH Keywords

signed graphGram matrixCoxeter spectrumDynkin typecorankedge-bipartite graphinflation algorithm

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Combinatorics in computer science (68R05) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Quadratic and bilinear forms, inner products (15A63) Algebraic aspects of posets (06A11) Signed and weighted graphs (05C22)

Related Items (17)

A Gram classification of principal Cox-regular edge-bipartite graphs via inflation algorithm ⋮ Coxeter Invariants for Non-negative Unit Forms of Dynkin Type 𝔸r ⋮ Symbolic computation of strong Gram congruences for Cox-regular positive edge-bipartite graphs with loops ⋮ On polynomial time inflation algorithm for loop-free non-negative edge-bipartite graphs ⋮ A Strong Gram Classification of Non-negative Unit Forms of Dynkin Type 𝔸r ⋮ Quadratic algorithm to compute the Dynkin type of a positive definite quasi-Cartan matrix ⋮ On mesh geometries of root Coxeter orbits and mesh algorithms for corank two edge-bipartite signed graphs ⋮ A Coxeter spectral classification of positive edge-bipartite graphs. II: Dynkin type \(\mathbb{D}_n\) ⋮ Coefficients of non-negative quasi-Cartan matrices, their symmetrizers and Gram matrices ⋮ Applications of mesh algorithms and self-dual mesh geometries of root Coxeter orbits to a Horn-Sergeichuk type problem ⋮ On the structure of loop-free non-negative edge-bipartite graphs ⋮ Root systems and inflations of non-negative quasi-Cartan matrices ⋮ Incidence graphs and non-negative integral quadratic forms ⋮ A computational technique in Coxeter spectral study of symmetrizable integer Cartan matrices ⋮ A Coxeter spectral classification of positive edge-bipartite graphs. I: Dynkin types \(\mathcal{B}_n\), \(\mathcal{C}_n\), \(\mathcal{F}_4\), \(\mathcal{G}_2\), \(\mathbb{E}_6\), \(\mathbb{E}_7\), \(\mathbb{E}_8\) ⋮ A Coxeter type classification of one-peak principal posets ⋮ A Graph Theoretical Framework for the Strong Gram Classification of Non-negative Unit Forms of Dynkin Type 𝔸n

Uses Software

• Maple
• Python

Cites Work

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