# Search results for: Xueliang Li

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

Linear Algebra and its Applications > 2016 > 497 > C > 199-208

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

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 > 497 > C > 199-208

The energy E(G) of a graph G is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. If a graph G of order n has the same energy as the complete graph Kn, i.e., if E(G)=2(n−1), then G is said to be borderenergetic. We obtain three asymptotically tight bounds on the edge number of borderenergetic graphs. Then, by using disconnected regular graphs we construct connected...

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...