2018年信息与数学学院学术报告(二十八)

讲座题目:On the spectral moments of signless Laplacian matrix of trees and unicyclic graphsance

主办单位:长江大学信息与数学学院

报告专家:吴亚平(江汉大学,副教授)

报告时间:2018119 周五下午15:30-17:00

报告地点:东校区8-400

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专家简介:吴亚平,女,理学博士,江汉大学副教授。2011年博士毕业于华中师范大学,研究方向为图论,主要兴趣是图的结构、图谱。主要研究成果发表在JGTLAA等国际权威期刊。

摘要:Let  be the signless Laplacian matrix of , where  is the adjacency matrix of  and  is the diagonal matrix of vertex degrees. Let   be the eigenvalues in non-increasing order of .  The number  is called the -th signless Laplacian spectral moment of , denoted by , and  is the sequence of signless Laplacian spectral moments of . For two graphs , , we shall write  if for some , and  hold. In this paper, we prove that the -order of a graph is monotonic on some transformations, and determine the first and the last graphs, in a -order,  of all trees and unicyclic graphs of order , respectively,   and finally  characterize the extremal graphs for trees of order  with diameter  and unicyclic graphs of order  with girth .