# Search results for: Xueliang Li

Linear Algebra and Its Applications > 2013 > 438 > 11 > 4547-4556

Linear Algebra and Its Applications > 2011 > 435 > 10 > 2334-2346

Journal of Mathematical Analysis and Applications > 2010 > 368 > 1 > 311-319

Linear Algebra and Its Applications > 2013 > 438 > 11 > 4547-4556

Given a graph G, let 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 study the skew energy of random oriented graphs and formulate an exact estimate of the skew energy for almost all oriented graphs by generalizing...

Linear Algebra and Its Applications > 2011 > 435 > 10 > 2334-2346

In 1970s, Gutman introduced the concept of the energy E(G) for a simple graph G, which is defined as the sum of the absolute values of the eigenvalues of G. This graph invariant has attracted much attention, and many lower and upper bounds have been established for some classes of graphs among which bipartite graphs are of particular interest. But there are only a few graphs attaining the equalities...

Journal of Mathematical Analysis and Applications > 2010 > 368 > 1 > 311-319

Gutman et al. introduced the concepts of energy E(G) and Laplacian energy EL(G) for a simple graph G, and furthermore, they proposed a conjecture that for every graph G, E(G) is not more than EL(G). Unfortunately, the conjecture turns out to be incorrect since Liu et al. and Stevanović et al. constructed counterexamples. However, So et al. verified the conjecture for bipartite graphs. In the present...