Discrete isopermetric problems and the related applications (Mingzu Zhang)

Abstract

The classical isoperimetric inequality in the Euclidean plane R^2 states that for a simple closed curve M of the length L_M, enclosing a region of the area A_M, one gets {L_M}^2geq4pi A_M. We will discuss discrete isopermetric problems of the power graph in both edge version and vertex version. The relationship between a continuous nowhere differentiable function, Takagi function, and the edge isopermetric problem of bijective connection network is given. The h-extra edge-connectivity of this graphs is also related to some problem about the level set of Takagi function, raised by Donald Knuth. D. Ellis and I. Leader discussed an edge isoperimetric inequality for antipodal subsets of the hypercube and we rewrite their results. We also investigate some properties of vertex isopermetric problem of hypercube. It is also related to the modified Takagi function and can be applied to calculate the h-extra connectivity of hypercube.

Joint work with Lianzhu Zhang, Xing Feng and Hong-Jian Lai.

Time

2018-07-18   14:00 ~ 15:00   

Speaker

Mingzu Zhang,  Xiamen University

Room

Room 602, School of Information Management & Engineering, Shanghai University of Finance & Economics