组合矩阵论和组合网络理论

The research project consists of several very much active topics in Combinatorial Matrix Theory, such as existence of matrices (extremal graph theory and degree sequences), spectral graph theory, sign pattern matrices, completely positive matrices, compact graphs, etc. Moreover, several.important parameters of Combinatorial Network Theory and optimal structures of double loop networks have been throughout investigated. In the past three years, 57 papers and a book on.interconnection networks have been published at home and abroad journals, 25 of which appeared in SCI journals. In Combinatorial Matrix theory, several variant classical Turán numbers of.extremal graph theory have been determined. These results develop and open new directions for extremal graph theory. On Laplacian matrices, a new invariant parameter, bounds for the second largest, k-th, the third, second smallest eigenvalues and the generalized Laplacian matrix of mixed.and signed graphs have been presented. Moreover, the Merris’ conjecture was confirmed. On the adjacency matrices, bounds for spectral radius of directed graphs are obtained and problems of.maximum (minimum) energy in chemical molecular graphs raised by Cvetkovic etc have been solved (partially). There are also breakthrough developments in sign pattern matrices, completely.positive matrices, normal Cayley graphs, L-sharp permutation groups. In combinatorial networks, the restricted vertex and restricted edge connectivity of transitive graphs and width-diameter, dominant number of some specific networks have been throughout studied. In general, the research has attained the lead level of the same kind international researches.

研究组合矩阵论中当今国际关注的几个重要问题；矩阵类存在性（或图的度序列）、谱图理论、符号模式矩阵、完全正矩阵、紧图和超紧图；组合网络理论中度量互连网络性能的几个重要参数：图的限制连通度、宽直径和（d，m）控制数等，和双环网络的最优结构。与图论、矩阵论、群论等数学分支联系密切。在计算机科学、物理、化学、经济学中应用广泛。