报告题目1：Spectra of power hypergraphs and signed graphs

报告人：卜长江教授，哈尔滨工程大学

报告时间：2023年9月24日（周日）9：00-10：00

报告地点：20-404

报告摘要：The hypergraph obtained by adding k-1 vertices of degree 1 on each edge of graph G is called the k-th power hypergraph G^(k) of G. The Perron-Frobenius theorem of tensors shows that the spectral radius of a connected hypergraph is one of its eigenvalues, but the multiplicity of the spectral radius is currently unknown. In this report, we generate all the eigenvalues of the power hypergraphs using the eigenvalues of the signed subgraphs of G, and provide a formula for the spectral moments of the power hypergraph G^(k)，which involves the number of subgraphs, the number of parity walks of G, and the parameter k. Using the above results, we give an expression for the characteristic polynomial of the power hypergraph and give the multiplicity of the spectral radius of the power hypergraph.

This is a joint work with Lixiang Chen and Edwin van Dam. 

报告人简介：卜长江，哈尔滨工程大学数学系教授，博士生导师。多年来一直从事组合数学与图论的研究，主要研究方向包括图与超图谱理论、组合张量、广义逆理论、复杂网络等。发表论文200余篇，在科学出版社出版专著4部，主持国家自然科学基金项目多项。现任中国运筹学会图论组合分会副理事长，中国数学会组合数学与图论学会理事，黑龙江省数学会常务理事。

报告题目2：Some extremal results on the α-spectral radius of digraphs

报告人：王力工教授，西北工业大学

报告时间：2023年9月24日（周日）10：00-11：00

报告地点：20-404

报告摘要：Let G be a digraph with adjacency matrix A(G). The matrix A_α(G) of a digraph G is defined as A_α(G) = αD(G) + (1 − α) A(G), for α∈[0, 1], where D(G) is the diagonal matrix with outdegrees of vertices of G. The largest modulus of the eigenvalues of A_α(G) is called the A_α spectral radius of G, denoted by λ_α(G). In this talk, we introduce some extremal results about the spectral radius λ_α(G) that generalize previous results about λ₀(G) and λ_1/2(G). We mainly characterize the extremal digraphs with the maximum (or minimum) A_α spectral radius among all-digrahs and -digraphs on n vertices. Furthermore, we determine the  digraphs with the second and the third minimum A_α spectral radius among all strongly connected bicyclic digraphs. For 0 ≤ α ≤ 1/2, we also determine the digraphs with the second, the third and the fourth minimum A_α spectral radius among all strongly connected digraphs on n vertices. Finally, we characterize the digraph with the minimum A_α spectral radius among all strongly connected bipartite digraphs which contain a complete bipartite subdigraph. This is a joint work with Weige Xi.

报告人简介：王力工，西北工业大学教授、博士生导师，荷兰特文特大学博士，研究方向为图论及其应用，主要研究包括：图谱理论，有向图与超图的谱性质，整树与整图的刻画，图的Turán数，图的Gallai-Ramsey数等。主持国家自然科学基金多项。在《Journal of Graph Theory》、《Electronic Journal of Combinatorics》、《Discrete Mathematics》、《Discrete Applied Mathematics》、《Linear Algebra and its Applications》等重要学术期刊发表SCI论文120多篇。