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
- State University of New York at Potsdam United States
- Binghamton University United States
Numerical Analysis, Algebra and Number Theory, 05C50 (Primary) 05C22, 05C25 (Secondary), Adjacency eigenvalues, Incidence matrix, Signless Laplacian, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Gain graph, Laplacian eigenvalues, Geometry and Topology, Combinatorics (math.CO), Laplacian matrix
Numerical Analysis, Algebra and Number Theory, 05C50 (Primary) 05C22, 05C25 (Secondary), Adjacency eigenvalues, Incidence matrix, Signless Laplacian, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Gain graph, Laplacian eigenvalues, Geometry and Topology, Combinatorics (math.CO), Laplacian matrix
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