88304am永利集团

Let X be a pure K+1-dimensional simplicial complex with orientation k,and s1 the k-up Laplacian spectral radius. In this talk, we investigate theupper and lower bounds on s1. On the one hand, we give an upper bound on s1. Moreover,if X is k+1-path connected, then characterize equality case. This generalizessome bounds on graph Laplacian to higher dimensions. On the other hand, we givea new lower bound on s1. This improves the lower bound given by Duval andReiner (2002). As a corollary, we also derive a lower bound for s1 in terms ofthe k+1-diameter d of X, which not only strengthens the previously known boundfor graphs (i.e., the case k=0), but also generalizes it to higher dimensions.

韩月丽，中南大学博士，导师是鲁卢副教授。主要研究方向是代数图论。目前，已在《Ars Math. Contemp.》、《Appl. Math. Comput.》期刊上发表论文两篇，在《Bull. Malays. Math. Sci. Soc.》期刊上接收论文一篇。