Hermitian adjacency spectrum and switching equivalence of mixed graphs

作者：Mohar Bojan

来源：Linear Algebra and Its Applications, 2016, 489: 324-340.

DOI：10.1016/j.laa.2015.10.018

• Mixed graph
• Digraph
• Hermitian adjacency matrix
• Spectral characterization
• Switching equivalence
• Eigenvalue
• Spectral radius

It is shown that an undirected graph G is cospectral with the Hermitian adjacency matrix of a mixed graph D obtained from a subgraph H of G by orienting some of its edges if and only if H = G and D is obtained from G by a four-way switching operation; if G is connected, this happens if and only if lambda(1) (G) = lambda(1) (D). All mixed graphs of rank 2 are determined and this is used to classify which mixed graphs of rank 2 are cospectral with respect to their Hermitian adjacency matrix. Several families of mixed graphs are found that are determined by their Hermitian spectrum in the sense that they are cospectral precisely to those mixed graphs that are switching equivalent to them.

• 出版日期2016-1-15