The Laplacian matching polynomials of graphs can be viewed as the average of Laplacian characteristic polynomials of all signed graphs. In this lecture，we determine all the limit points of the largest Laplacian matching roots of graphs less than 4.38, and characterize the connected graphs with the largest Laplacian matching roots less than 2 + \sqrt{5}.

王建锋，山东理工大学教授、博士生导师，数学与统计学院副院长，山东省泰山学者，主要从事图谱理论、图多项式等方面的研究, 在Adv. Appl. Math、J. Graph Theory、J. Algebraic Combin、Electron J. Combin.等发表论文90余篇，先后主持国家自然科学基金4项；现任CSIAM图论组合及应用专委会、信息和通讯领域的数学专委会委员等。