On the determinant of the Laplacian matrix of a complex unit gain graph

DOI10.1016/j.disc.2017.07.003zbMath1372.05097OpenAlexW2739914937MaRDI QIDQ2411597

Shi-Cai Gong, Yi Wang, Yi-Zheng Fan

Publication date: 24 October 2017

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2017.07.003

zbMATH Keywords

adjacency matrixdeterminantLaplacian matrixgain graph

Mathematics Subject Classification ID

Signed and weighted graphs (05C22)

Related Items

Principal Minors of Hermitian (Quasi-)Laplacian Matrix of Second Kind for Mixed Graphs ⋮ Bounds for the rank of a complex unit gain graph in terms of the independence number ⋮ On the relation between the adjacency rank of a complex unit gain graph and the matching number of its underlying graph ⋮ On the adjacency matrix of a complex unit gain graph ⋮ Complex unit gain graphs of rank 2 ⋮ The rank of a complex unit gain graph in terms of the matching number ⋮ Unnamed Item ⋮ The multiplicity of an \(A_\alpha \)-eigenvalue: a unified approach for mixed graphs and complex unit gain graphs ⋮ Inertia indices of a complex unit gain graph in terms of matching number ⋮ The spectral property of hypergraph coverings ⋮ NEPS of complex unit gain graphs ⋮ On connected \(\mathbb{T}\)-gain graphs with rank equal to girth ⋮ Unnamed Item ⋮ Complex unit gain graphs with exactly one positive eigenvalue ⋮ Bounds for the rank of a complex unit gain graph in terms of its maximum degree ⋮ Spectra of quaternion unit gain graphs ⋮ Bounds for the extremal eigenvalues of gain Laplacian matrices ⋮ Unnamed Item ⋮ Balancedness and the least Laplacian eigenvalue of some complex unit gain graphs ⋮ GRAPHS DETERMINED BY THEIR -GAIN SPECTRA

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