[기타] 12월 4일 수학과 colloquium 안내
- 자연과학대학교학팀
- 이서안
- 작성일 2020-11-30
- 조회수 4951
※연사 : 박종육 (경북대학교)
※일시 : 12월 4일(금) 5:00-6:00 PM
※방법 : Zoom URL
https://ajou-ac-kr.zoom.us/j/ https://ajou-ac-kr.zoom.us/j/
강연제목: On the clique number of 2-walk-regular graphs
초록:
In this talk, we consider the question of when a strongly regular graph with parameters $((s+1)(st+1),s(t+1),s-1,t+1)$ can exist. A strongly regular graph with such parameters is called a pseudo-generalized quadrangle. A pseudo-generalized quadrangle can be derived from a generalized quadrangle, but there are other examples which do not arise in this manner. If the graph is derived from a generalized quadrangle then $t \leq s^2$ and $s \leq t^2$, while for pseudo-generalized quadrangles we still have the former bound but not the latter. Previously, Neumaier has proved a bound for $s$ which is cubic in $t$, but we improve this to one which is quadratic. The proof involves a careful analysis of cliques and cocliques in the graph. This improved bound eliminates many potential parameter sets which were otherwise feasible.