Arithmetical structures on graphs

DOI10.1016/j.laa.2017.09.018zbMath1428.05188arXiv1604.02502OpenAlexW2962877946WikidataQ121840378 ScholiaQ121840378MaRDI QIDQ2412696

Hugo Corrales, Carlos E. Valencia

Publication date: 27 October 2017

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

Full work available at URL: https://arxiv.org/abs/1604.02502

zbMATH Keywords

Catalan numbercyclepath\(M\)-matricesdelta-wye transformationedge subdivisionarithmetical structuresclique-star transformationmerging verticessplitting vertices

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Algebraic combinatorics (05E99) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Positive matrices and their generalizations; cones of matrices (15B48) Matrices, determinants in number theory (11C20) Graph operations (line graphs, products, etc.) (05C76)

Related Items (15)

Minimal free resolutions of lattice ideals of digraphs ⋮ Arithmetical structures on graphs with connectivity one ⋮ Abelian networks IV. Dynamics of nonhalting networks ⋮ Counting arithmetical structures on paths and cycles ⋮ Algorithmic aspects of arithmetical structures ⋮ Arithmetical structures on graphs ⋮ Arithmetical structures on bidents ⋮ Critical groups of arithmetical structures on star graphs and complete graphs ⋮ Arithmetical structures on dominated polynomials ⋮ The critical polynomial of a graph ⋮ Chip-Firing Games and Critical Groups ⋮ The extremal spectral radii of the arithmetical structures on paths ⋮ Bounding the number of arithmetical structures on graphs ⋮ On arithmetical structures on complete graphs ⋮ Critical groups of arithmetical structures under a generalized star-clique operation

Cites Work

• Smith normal form and Laplacians
• Arithmetical graphs
• Chip-firing and energy minimization on M-matrices
• Arithmetical structures on graphs
• On the critical ideals of graphs
• Algebraic Potential Theory on Graphs
• Degree and Algebraic Properties of Lattice and Matrix Ideals
• Catalan Numbers
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