On the Laplacian Eigenvalues of Signed Graphs

By Yaoping Hou, Jiongsheng Li, Yong-Liang Pan. 2003

160 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Organic Chemistry

View Paper: https://www.semanticscholar.org/paper/7c57004f082b3e0694917ec0917a5b7dd69da7d3

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In Computational Theory and Mathematics

In Geometry and Topology

In Organic Chemistry

Citations in the corpus

Bounds for the Least Laplacian Eigenvalue of a Signed Graph (2005, background): “In [10] the largest eigenvalue λmax(Γ) was investigated and in this section we focus our attention on the least eigenvalue of a signed graph.”
Consensus Problems on Networks With Antagonistic Interactions (2013, methodology): “The definition used in this paper for a Laplacian in the case of signed is , where in the connectivity matrix the weights are in absolute value, see [24], [31].”
Matrices in the Theory of Signed Simple Graphs (2013, background): “Here are some of their results: Theorem IV.6 (Hou, Li, and Pan [16]).”
Maximizing spectral radius of unoriented Laplacian matrix over bicyclic graphs of a given order (2008, methodology): “In this sense, there is much overlap between the work of [1,11,12] on mixed graphs and the work of [9] (and other papers) on signed graphs.”
Unoriented Laplacian maximizing graphs are degree maximal (2008, background): “The concepts of oriented or unoriented Laplacian matrix for a graph have also been extended to Laplacian matrix of a mixed graph or of a signed graph (see [2,19,30,31]).”
Spectral properties of complex unit gain graphs (2011, background): “This generalizes a signed graphic version that appears in [9], which generalizes the unsigned graphic relation: λ1(L( )) λ1(Q( )).”
On the consensus and bipartite consensus in high-order multi-agent dynamical systems with antagonistic interactions (2014, background): “This latter property means [1, 13, 33] that the set of vertices V can be partitioned into two disjoint subsets V1 and V2 such that for every i, j ∈ Vp, p ∈ [1, 2], [A]ij ≥ 0, while for every i ∈ Vp, j ∈ Vq, p, q ∈ [1, 2], p 6= q, [A]ij ≤ 0.”