数学系 Seminar 第 2021 期
数学系“60周年”系庆系列报告
报告主题：Asymptotic values of four Laplacian-type energies for matrices with degree-distance-based entries of random graphs
报告人：李学良 教授 （南开大学）
报告时间：2020年10月27日（周二） 14:00-15:15
参会方式：腾讯 会议
会议ID：873 777 5758
主办部门：理学院数学系
报告摘要： Let $f(D(i, j), d_i, d_j)$ be a real function symmetric in $i$ and $j$ with the property that $f((d, 1+o(1))np, (1+o(1))np)=(1+o(1))f(d, np, np)$ for $d=1,2$. Let $G$ be a graph, $d_i$ denote the degree of a vertex $i$ of $G$ and $D(i, j)$ denote the distance between vertices $i$ and $j$ in $G$. In this talk, we define the $f$-weighted Laplacian matrix for random graphs in the Erd$\ddot{o}$s-R$\acute{e}$nyi random graph model $\mathcal{G}_{n, p}$, where $p\in (0, 1)$ is fixed. Four weighted Laplacian type energies: the weighted Laplacian energy $\mathscr{LE}_f(G)$, weighted signless Laplacian energy $\mathscr{LE}^{+}_f(G)$, weighted incidence energy $\mathscr{IE}_f(G)$ and the weighted Laplacian-energy like invariant $\mathscr{LEL}_f(G)$ are introduced and studied. We obtain the asymptotic values of $\mathscr{IE}_f(G)$ and $\mathscr{LEL}_f(G)$, and the values of $\mathscr{LE}_f(G)$ and $\mathscr{LE}_f^{+}(G)$ under the condition that $f(D(i, j), d_i, d_j)$ is a function dependent only on $D(i, j)$.
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