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讲座名称：Ordering Q-indices of graphs: given size and girth

讲座人：黄琼湘 教授

讲座时间：10月31日15:00

讲座地点：腾讯皇冠hg666体育议直播（ID:613 582 169）

讲座人介绍：

黄琼湘，新疆大学数学与系统科学ku酷游app入口,亚博app,皇冠hg666体育教授，博士生导师，1995年获四川大学理学博士学位，1998年9月至1999年2月在中科院系统所晨兴组合研究中心访问，2003年至 2017年担任数ku酷游app入口,亚博app,皇冠hg666体育副院长，现担任新疆数学学皇冠hg666体育秘书长。

近年来主要从事代数图论，特别是图谱理论的研究。主持并完成国家自然科学基金面上项目3项，重点项目子项目1项。在 J. Combin. Theory Ser. B，Europ. J. Combin.，J. Algebraic Combin.，Discrete Math.， Discrete Appl. Math.，ACTA Math. Sinica，Linear Algebra Appl.等主流学术期刊上发表论文120余篇，其中SCI收录70 余篇。

讲座内容：

The signless Laplacian matrix in graph spectra theory is extensively studied by researchers. In 1981, Cvetkovi\'{c} pointed $12$ directions in further investigations of graph spectra, one of which is ``classifying and ordering graphs''. Along with this classic direction, we pay our attention on the order of the largest eigenvalue of the signless Laplacian matrix of graphs, which is usually called the $Q$-index of a graph. Let $\mathbb{G}(m, g)$ (resp. $\mathbb{G}(m, \geq g)$) be the family of connected graphs on $m$ edges with girth $g$ (resp. no less than $g$), where $g\ge3$.

In this talk, we firstly order the first $(\lfloor\frac{g}{2}\rfloor+2)$ largest $Q$-indices of graphs in $\mathbb{G}(m, g)$, where $m\ge 3g\ge 12$. Secondly, we order the first $(\lfloor\frac{g}{2}\rfloor+3)$ largest $Q$-indices of graphs in $\mathbb{G}(m, \geq g)$, where $m\ge 3g\ge 12$. As a complement, we give the first five largest $Q$-indices of graphs in $\mathbb{G}(m, 3)$ with $m\ge 9$. Finally, we give the order of the first eleven largest $Q$-indices of all connected graphs with size $m$.

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