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- W2511355758 abstract "A mixed graph is obtained from an undirected graph by orienting a subset of its edges. The Hermitian adjacency matrix of a mixed graph M of order n is an n × n matrix H ( M ) = ( h k l ) , where h k l = - h l k = i ( i = - 1 ) if there exists an orientation from vk to vl and h k l = h l k = 1 if there exists an edge between vk and vl but not exist any orientation, and h k l = 0 otherwise. Let D ( M ) = d i a g ( d 1 , d 2 , ź , d n ) be a diagonal matrix where di is the degree of vertex vi in the underlying graph Mu. Hermitian matrices L ( M ) = D ( M ) - H ( M ) , Q ( M ) = D ( M ) + H ( M ) are said as the Hermitian Laplacian matrix, Hermitian quasi-Laplacian matrix of mixed graph M, respectively. In this paper, it is shown that they are positive semi-definite. Moreover, we characterize the singularity of them. In addition, an expression of the determinant of the Hermitian (quasi-)Laplacian matrix is obtained." @default.
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- W2511355758 date "2017-01-01" @default.
- W2511355758 modified "2023-09-26" @default.
- W2511355758 title "Singularity of Hermitian (quasi-)Laplacian matrix of mixed graphs" @default.
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- W2511355758 doi "https://doi.org/10.1016/j.amc.2016.08.032" @default.
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