报告题目：D^Q-integral and D^L-integral generalized wheel graphs

主讲人：王力工教授

时 间：2024年1月27日（周六）上午09：15

地 点：基础楼317学习室

主办单位：理学院

主讲人简介：

王力工，西北工业大学教授、博士生导师，荷兰Twente大学博士，研究方向为图论及其应用，主要研究包括：图谱理论，有向图与超图的谱性质，整图的刻画，图的Turán数，图的Gallai-Ramsey数等，主持国家自然科学基金多项，在《Journal of Graph Theory》、《Discrete Mathematics》、《Discrete Applied Mathematics》、《Electronic Journal of Combinatorics》、《Linear Algebra and its Applications》等国内外重要学术期刊发表SCI论文120多篇。

摘要:

A graph G is said to be M-integral (resp. A-integral, D-integral, D^L-integral or D^Q-integral) if all eigenvalues of its matrix M (resp. adjacency matrix A(G), distance matrix D(G), distance Laplacian matrix D^L(G) or distance signless Laplacian matrix D^Q(G)) are integers. Lu et al. [Discrete Math, 346 (2023)] defined the generalized wheel graph GW(a,m,n) as the graph aKm∇Cn, and obtained all D-integral generalized wheel graphs aKm∇Cn. Based on the above research, in this paper, we determine all D^L-integral and D^Q-integral generalized wheel graphs aKm∇Cn respectively. As byproducts, we give a sufficient and necessary condition for the join of regular graphs G1∇G2 to be D^L-integral, from which we can get infinitely many new classes of D^L-integral graphs according to the large number of research results about the A-integral graphs. This is a joint work with Yirui Chai and Yuwei Zhou.