Hermitian adjacency spectrum and switching equivalence of mixed graphs

13 May 2015 Mohar Bojan

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... (read more)

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