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}^2\geq4\pi 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

7月18日（周三）14:00-15:00

Speaker

Mingzu Zhang received the M.S. degree in mathematics from Xinjiang University, Urumqi, China, in 2014, and the B.S. degree in mathematics from the Tianjin University of Technology and Education, Tianjin, China, in 2010. He is currently working toward the Ph.D. degree in mathematics at the School of Mathematical Science, Xiamen University, Xiamen, China.

His research interests include the area of graph theory, influence of boolean function and fault-tolerance of networks.

Venue

信息管理与工程学院  602室

上海财经大学

上海市杨浦区武东路100号