# Search results for: Xueliang Li

Linear Algebra and its Applications > 2017 > 519 > C > 343-365

Linear Algebra and its Applications > 2016 > 496 > C > 475-486

Linear Algebra and Its Applications > 2015 > 466 > Complete > 182-207

Linear Algebra and its Applications > 2017 > 519 > C > 343-365

Let G be a mixed graph with n vertices, H(G) the Hermitian adjacency matrix of G, and λ1(G),λ2(G),…,λn(G) the eigenvalues of H(G). The Hermitian energy of G is defined as EH(G)=∑i=1n|λi(G)|. In this paper we characterize the limiting spectral distribution of the Hermitian adjacency matrices of random mixed graphs, and as an application, we give an estimation of the Hermitian energy for almost all...

Linear Algebra and its Applications > 2016 > 496 > C > 475-486

Let G be a simple undirected graph, and Gϕ be a mixed graph of G with the generalized orientation ϕ and Hermitian-adjacency matrix H(Gϕ). Then G is called the underlying graph of Gϕ. The Hermitian energy of the mixed graph Gϕ, denoted by EH(Gϕ), is defined as the sum of all the singular values of H(Gϕ). A k-regular mixed graph on n vertices having Hermitian energy nk is called a k-regular optimum...

Linear Algebra and Its Applications > 2015 > 466 > Complete > 182-207

A complex adjacency matrix of a mixed graph is introduced in the present paper, which is a Hermitian matrix and called the Hermitian-adjacency matrix. It incorporates both adjacency matrix of an undirected graph and skew-adjacency matrix of an oriented graph. Some of its properties are studied. Furthermore, properties of its characteristic polynomial are studied. Cospectral problems among mixed graphs,...