Hermitian adjacency spectrum and switching equivalence of mixed graphs
Hermitian adjacency spectrum and switching equivalence of mixed graphs
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DOI：
10.1016/j.laa.2015.10.018
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发表时间：
2015-05
影响因子：
1.1
通讯作者：
B. Mohar
中科院分区：
文献类型：
--
作者：
B. Mohar
证明了无向图G与混合图D的Hermitian邻接矩阵是共谱的当且仅当H= G且D是由G通过四路转换运算得到的;如果G是连通的，则当且仅当λ 1（G）= λ 1（D）.所有的秩2的混合图的确定，这是用来分类的秩2的混合图是关于他们的埃尔米特邻接矩阵的共谱。几个家庭的混合图被发现，确定由他们的厄米特谱的意义上，他们是共谱精确到那些混合图，是切换等价于他们。
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 λ 1 (G)= λ 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.