# Search results for: Xueliang Li

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

Linear Algebra and Its Applications > 2013 > 439 > 10 > 2948-2960

Linear Algebra and Its Applications > 2010 > 432 > 5 > 1144-1146

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 > 2013 > 439 > 10 > 2948-2960

Let G be a simple undirected graph, and Gσ be an oriented graph of G with the orientation σ and skew-adjacency matrix S(Gσ). The skew energy of the oriented graph Gσ, denoted by ES(Gσ), is defined as the sum of the absolute values of all the eigenvalues of S(Gσ). In this paper, we characterize the underlying graphs of all 4-regular oriented graphs with optimum skew energy and give orientations of...

Linear Algebra and Its Applications > 2010 > 432 > 5 > 1144-1146

For a simple graph G, the energy E(G) is defined as the sum of the absolute values of all the eigenvalues of its adjacency matrix A(G). Let n,m, respectively, be the number of vertices and edges of G. One well-known inequality is that E(G)⩽λ1+(n-1)(2m-λ1), where λ1 is the spectral radius. If G is k-regular, we have E(G)⩽k+k(n-1)(n-k). Denote E0=k+k(n-1)(n-k). Balakrishnan [R. Balakrishnan, The energy...