Spectral properties of complex unit gain graphs
Copyright policy )Spectral properties of complex unit gain graphs
A complex unit gain graph is a graph where each orientation of an edge is given a complex unit, which is the inverse of the complex unit assigned to the opposite orientation. We extend some fundamental concepts from spectral graph theory to complex unit gain graphs. We define the adjacency, incidence and Laplacian matrices, and study each of them. The main results of the paper are eigenvalue bounds for the adjacency and Laplacian matrices.
13 pages, 1 figure, to appear in Linear Algebra Appl
- Binghamton University United States
Numerical Analysis, incidence matrix, Algebra and Number Theory, Graphs and linear algebra (matrices, eigenvalues, etc.), 05C50 (Primary) 05C22, 05C25 (Secondary), gain graph, Adjacency eigenvalues, signless Laplacian, Incidence matrix, Signed and weighted graphs, Graphs and abstract algebra (groups, rings, fields, etc.), Signless Laplacian, adjacency eigenvalues, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Gain graph, Laplacian eigenvalues, Geometry and Topology, Combinatorics (math.CO), Laplacian matrix
Numerical Analysis, incidence matrix, Algebra and Number Theory, Graphs and linear algebra (matrices, eigenvalues, etc.), 05C50 (Primary) 05C22, 05C25 (Secondary), gain graph, Adjacency eigenvalues, signless Laplacian, Incidence matrix, Signed and weighted graphs, Graphs and abstract algebra (groups, rings, fields, etc.), Signless Laplacian, adjacency eigenvalues, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Gain graph, Laplacian eigenvalues, Geometry and Topology, Combinatorics (math.CO), Laplacian matrix
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