The weighted complexity and the determinant functions of graphs

DOI10.1016/j.laa.2010.03.001zbMath1203.05064arXiv0705.2284OpenAlexW2080309196MaRDI QIDQ975601

Jaeun Lee, Young Soo Kwon, Dong Seok Kim

Publication date: 10 June 2010

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

Full work available at URL: https://arxiv.org/abs/0705.2284

zbMATH Keywords

characteristic polynomialweighted graphszeta functionBartoldi zeta functiondeterminant functionsweighted complexity

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Signed and weighted graphs (05C22) Graph operations (line graphs, products, etc.) (05C76)

Related Items (2)

A note on Bartholdi zeta function and graph invariants based on resistance distance ⋮ The partial differential coefficients for the second weighted Bartholdi zeta function of a graph

Cites Work

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• Generalized characteristic polynomials of graph bundles
• Line-digraphs, arborescences and theorems of Tutte and Knuth
• On the weighted complexity of a regular covering of a graph
• A note on the zeta function of a graph
• Counting paths in graphs
• Laplacian spectra and spanning trees of threshold graphs
• A Combinatorial Proof of the All Minors Matrix Tree Theorem
• The $Q$-spectrum and spanning trees of tensor products of bipartite graphs
• Graphs and Matrices
• A Contribution to the Theory of Chromatic Polynomials

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