Construction of divisible design graphs using affine designs
主 讲 人 :Vladislav Kabanov 研究员
活动时间:07月23日15时35分
地 点 :球友会D203报告厅
讲座内容:
A $k$-regular graph with $v$ vertices is a {\em divisible design graph with parameters} $(v,k,\lambda_1,\lambda_2,m,n)$ if its vertex set can be partitioned into $m$ classes of size $n$ such that any two different vertices from the same class have $\lambda_1$ common neighbours, and any two vertices from different classes have $\lambda_2$ common neighbours. Divisible design graphs were introduced by H. Kharaghani and first provided by W.H. Haemers, H. Kharaghani and M. Meulenberg. In particular, the authors have proposed several constructions of divisible design graphs using various combinatorial structures. Some new combinatorial constructions of divisible design graphs were later provided by many authors.In this talk, we present two prolific constructions that produce infinite series of divisible design graphs. Using affine designs for these constructions develops ideas of W.D. Wallis, D.G. Fon-Der-Flaass, and M. Muzychuk.
主讲人介绍:
Vladislav Kabanov is a Chief Researcher at Krasovskii Institute of Mathematics and Mechanics (Russian Academy of Sciences). His main research interests include finite simple groups, finite permutation groups, claw-free graphs, strongly regular graphs, Deza graphs, divisible design graphs, Star graphs, equitable partitions and eigenfunctions of graphs, Paley graphs and their generalisations.