Abstract
A mixed graph is a graph with undirected and directed edges. Guo and Mohar in 2017 determined all mixed graphs whose Hermitian spectral radii are less than 2. In this paper, we give a sufficient condition which can make Hermitian spectral radius of a connected mixed graph strictly decreasing when an edge or a vertex is deleted, and characterize all mixed graphs with Hermitian spectral radii at most 2 and with no cycle of length 4 in their underlying graphs.
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The authors are very grateful to the referee for his/her valuable comments.
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This work was supported by National Natural Science Foundation of China (11771016, 11871073).
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Yuan, BJ., Wang, Y., Gong, SC. et al. On Mixed Graphs Whose Hermitian Spectral Radii are at Most 2. Graphs and Combinatorics 36, 1573–1584 (2020). https://doi.org/10.1007/s00373-020-02181-w
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DOI: https://doi.org/10.1007/s00373-020-02181-w