On products and line graphs of signed graphs, their eigenvalues and energy
By K. A. Germina, K. ShahulHameed, Thomas Zaslavsky. 2010
109 citations recorded by the source corpus.
Abstract In this article we examine the adjacency and Laplacian matrices and their eigenvalues and energies of the general product (non-complete extended p -sum, or NEPS) of signed graphs. We express the adjacency matrix of the product in terms of the Kronecker matrix product and the eigenvalues and energy of the product in terms of those of the factor graphs. For the Cartesian product we characterize balance and compute expressions for the Laplacian eigenvalues and Laplacian energy. We give exact results for those signed planar, cylindrical and toroidal grids which are Cartesian products of signed paths and cycles. We also treat the eigenvalues and energy of the line graphs of signed graphs, and the Laplacian eigenvalues and Laplacian energy in the regular case, with application to the line graphs of signed grids that are Cartesian products and to the line graphs of all-positive and all-negative complete graphs.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Organic Chemistry
View Paper: https://www.semanticscholar.org/paper/bb6403c5b64bba3422d729e237a46fbc62e6ab07
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Citations in the corpus
- A Mathematical Bibliography of Signed and Gain Graphs and Allied Areas (2018, methodology): “184 (1998), 205–212. MR 99e:05056. Zbl 957.05046. An algorithm, based in part on Gerards (1994a), that, given an allnegative signed graph, finds a subdivided −K4 subgraph or a 3-coloring of the underlying graph.”
- Spectral properties of complex unit gain graphs (2011, background): “Recently there has been a growing study of matrices associated to a signed graph [9, 8, 10, 11, 17, 5].”