Spectral Properties of Dual Complex Unit Gain Graphs

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.