Spectral Properties of Complex Unit Gain Graphs

Details Spectral Properties of Complex Unit Gain Graphs Spectral Properties of Complex Unit Gain Graphs

2011-10-20

arxiv.org/abs/1110.4554v2

Mathematics

Combinatorics

13 pages, 1 figure, to appear in Linear Algebra Appl

Scientific paper

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.

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