Spectral Properties of Dual Complex Unit Gain Graphs
arxiv(2024)
摘要
In this paper, we study dual complex unit gain graphs and their spectral
properties. We establish the interlacing theorem for dual complex unit gain
graphs, and show that the spectral radius of a dual complex unit gain graph is
always not greater than the spectral radius of the underlying graph, and these
two radii are equal if and only if the dual complex unit gain graph is
balanced. Similar results hold for the spectral radius of the Laplacian matrix
of the dual complex unit gain graph too.
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