On the Laplacian Eigenvalues of Signed Graphs
From MaRDI portal
Publication:4804461
DOI10.1080/0308108031000053611zbMath1020.05044OpenAlexW2057551763MaRDI QIDQ4804461
Jiong-Sheng Li, Yao-Ping Hou, Yong-Liang Pan
Publication date: 28 April 2003
Published in: Linear and Multilinear Algebra (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/0308108031000053611
Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Signed and weighted graphs (05C22)
Related Items (66)
On adjacency and Laplacian cospectral non-isomorphic signed graphs ⋮ A spectral method to incidence balance of oriented hypergraphs and induced signed hypergraphs ⋮ Unnamed Item ⋮ Structure and stability of the equilibrium set in potential-driven flow networks ⋮ Negative (and positive) circles in signed graphs: a problem collection ⋮ Controllability of multi-agent systems with directed and weighted signed networks ⋮ Fixed-time bipartite consensus of multi-agent systems with disturbances ⋮ On the sum of Laplacian eigenvalues of a signed graph ⋮ Bipartite tracking consensus for multi-agent systems with Lipschitz-type nonlinear dynamics ⋮ Bounds for the rank of a complex unit gain graph in terms of the independence number ⋮ Prescribed performance bipartite consensus for nonlinear agents with antagonistic interactions: a PI transformation approach ⋮ On the determinant of the Laplacian matrix of a complex unit gain graph ⋮ Group-bipartite consensus of heterogeneous multi-agent systems over signed networks ⋮ The rank of a signed graph in terms of the rank of its underlying graph ⋮ Opinion dynamics with the increasing peer pressure and prejudice on the signed graph ⋮ Unnamed Item ⋮ Bipartite synchronization for inertia memristor-based neural networks on coopetition networks ⋮ A note on the nullity of unicyclic signed graphs ⋮ Bounds for the matching number and cyclomatic number of a signed graph in terms of rank ⋮ Stochastic fixed‐time formation for nonlinear multi‐agent systems under a discontinuous protocol ⋮ Graph-theoretic approaches for analyzing the resilience of distributed control systems: a tutorial and survey ⋮ Signed graphs with cut points whose positive inertia indexes are two ⋮ Spectral properties of complex unit gain graphs ⋮ On the rank of weighted graphs ⋮ Correction to: ``Restructured class of estimators for population mean using an auxiliary variable under simple random sampling scheme. A remark on normalized Laplacian eigenvalues of signed graph ⋮ The signed graphs with all but at most three eigenvalues equal to \(-1\) ⋮ Spreading and Structural Balance on Signed Networks ⋮ Maximizing spectral radius of unoriented Laplacian matrix over bicyclic graphs of a given order ⋮ On the spectrum of the normalized Laplacian for signed graphs: interlacing, contraction, and replication ⋮ Finite-/fixed-time bipartite consensus for first-order multi-agent systems via impulsive control ⋮ Unnamed Item ⋮ Finite-time and fixed-time bipartite consensus of multi-agent systems under a unified discontinuous control protocol ⋮ More on spectral analysis of signed networks ⋮ On the Bipartite Consensus of Higher-Order Multi-agent Systems with Antagonistic Interactions and Switching Topologies ⋮ On the consensus and bipartite consensus in high-order multi-agent dynamical systems with antagonistic interactions ⋮ Unoriented Laplacian maximizing graphs are degree maximal ⋮ Bounds for the rank of a complex unit gain graph in terms of its maximum degree ⋮ Projecting signed two-mode networks ⋮ No signed graph with the nullity \(\eta(G,\sigma)=|V(G)|-2m(G)+2c(G)-1\) ⋮ Eigenvalues of 2-edge-coverings ⋮ Spectra of quaternion unit gain graphs ⋮ The nullity of bicyclic signed graphs ⋮ A remark on eigen values of signed graph ⋮ Largest eigenvalue of a unicyclic mixed graphs ⋮ On graphs whose least eigenvalue is greater than –2 ⋮ Graphs with maximal signless Laplacian spectral radius ⋮ On the reduced signless Laplacian spectrum of a degree maximal graph ⋮ Laplacian of a graph covering and its applications ⋮ Signed \(k\)-uniform hypergraphs and tensors ⋮ On the least eigenvalue of a unicyclic mixed graph ⋮ Cheeger constants, structural balance, and spectral clustering analysis for signed graphs ⋮ Nonlinear finite-time bipartite consensus protocol for multi-agent systems associated with signed graphs ⋮ On the symmetry of the Laplacian spectra of signed graphs ⋮ Signed graphs with small positive index of inertia ⋮ On Laplacian equienergetic signed graphs ⋮ Adjacency rank and independence number of a signed graph ⋮ Restructured class of estimators for population mean using an auxiliary variable under simple random sampling scheme ⋮ Consensus for clusters of agents with cooperative and antagonistic relationships ⋮ Integral signed subcubic graphs ⋮ Relation between the rank of a signed graph and the rank of its underlying graph ⋮ Spectra of signed graphs ⋮ Signed complete graphs with exactly \(m\) non-negative eigenvalues ⋮ Bounds for the least Laplacian eigenvalue of a signed graph ⋮ The inertia indices of a signed graph in terms of the inertia indices of its underlying graph ⋮ Spectral characterizations of signed lollipop graphs ⋮ Signed graphs with extremal least Laplacian eigenvalue
Cites Work
- A note on Laplacian graph eigenvalues
- On the Laplacian eigenvalues of a graph
- Signed graphs
- Laplacian matrices of graphs: A survey
- Signed graphs, root lattices, and Coxeter groups
- An always nontrivial upper bound for Laplacian graph eigenvalues
- On the notion of balance of a signed graph
- A note on the second largest eigenvalue of the laplacian matrix of a graph∗
- Eigenvalues of the Laplacian of a graph∗
- A Combinatorial Proof of the All Minors Matrix Tree Theorem
- Eigenvalues and the degree sequences of graphs
This page was built for publication: On the Laplacian Eigenvalues of Signed Graphs