Graphs whose adjacency matrices have rank equal to the number of distinct nonzero rows

DOI10.1016/j.laa.2012.06.027zbMath1282.05120OpenAlexW2020746988MaRDI QIDQ389670

Shu-Hui Wu, Liang-Hao Huang, Bit-Shun Tam

Publication date: 21 January 2014

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

Full work available at URL: https://doi.org/10.1016/j.laa.2012.06.027

zbMATH Keywords

adjacency matrixrankreduced graphcographneighborhood equivalence classesnumber of distinct nonzero rowsreduced adjacency matrix

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (10)

On connected graphs of order \(n\) with girth \(g\) and nullity \(n-g\) ⋮ Graphs \(G\) with nullity \(n(G) - g(G) -1\) ⋮ On the algorithmic complexity of zero-sum edge-coloring ⋮ On connected signed graphs with rank equal to girth ⋮ Graphs with least eigenvalue \(-2\): ten years on ⋮ -cospectrality and -energy in cographs ⋮ On the nullity of a connected graph in terms of order and maximum degree ⋮ Spectral properties of cographs andP₅-free graphs ⋮ Cographs: eigenvalues and Dilworth number ⋮ Graphs \(G\) with nullity \(2c(G) + p(G) - 1\)

Cites Work

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• A characterization of graphs with rank 5
• Theorems on partitioned matrices revisited and their applications to graph spectra
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• On the rank of a cograph
• Unoriented Laplacian maximizing graphs are degree maximal
• Graph derivatives
• The neighborhood inclusion structure of a graph
• The rank of a cograph
• The minimum rank of matrices and the equivalence class graph
• Matrix Analysis
• Graph Classes: A Survey

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