## Combinatorics Research Group in Xiamen

The research interests of our group are in combinatorial theory (algebraic combinatorics and enumerative combinatorics), graph theory (algebraic graph theory, matching theory,digraphs, connectivity of graphs, random walks on graphs) and knot theory (invariants of knots and combinatorial knot theory), as well as their applications in mathematical chemistry, statistical physics and computer science. We have seminars since 2004. Now our group mainly consists of seven professors: Fuji Zhang, Xiaofeng Guo, Lianzhu Zhang, Jianguo Qian, Xian'an Jin, Weigen Yan, Haiyan Chen, two associate professors, Liqiong Xu, Litao Guo, two assistant professors Weiling Yang, Yuan-Hsun Lo.

2015-7-20

## 讨论班信息

2017秋季图论讨论班

Time：15:00-17:00, Thursday afternoon

Venue：Room 105,  Lab Building

12 Oct

Spanning Forest Complexes and f-vectors  I

by M. Asif

19 Oct

Spanning Forest Complexes and f-vectors  II

by M. Asif

26 Oct

Knot graphs

by Qi Yan

(Room 108, Lab Building)

1 Nov

青海师范大学

9 Nov

Discrete isopermetric problems and the related applications

by 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 ${L_M}^2\geq4\pi A_M$. 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.

2016