Layout of random circulant graphs

关于随机循环伯努利矩阵的奇异性概率

On the singularity probability of random circulant Bernoulli matrices

该研究针对所有概率参数取值，完整刻画了随机循环伯努利矩阵的渐近奇异性概率，填补了相关理论空白。

Embedding into Special Classes of Cyclic Graphs and its Applications in VLSI Layout

Graph embedding is the major technique which is used to map guest graph into host graph. In architecture simulation, graph embedding is said to be one of the strongest application for the execution of parallel algorithm and simulation of various interconnection networks \cite{Pa99}. In this paper, we have embedded circulant networks into star of cycle and folded hypercube into cycle-of-ladders and compute its exact wirelength. Further we have discussed the embedding parameters in VLSI Layout.

The asymptotic trace norm of random circulants and the graph energy

We compute the expected normalized trace norm (matrix/graph energy) of random symmetric band circulant matrices and graphs in the limit of large sizes, and obtain explicit bounds on the rate of convergence to the limit, and on the probabilities of large deviations. We also show that random symmetric band Toeplitz matrices have the same limit norm assuming that their band widths remain small relative to their sizes. We compare the limit norms across a range of related random matrix and graph ensembles.

Diameters of random circulant graphs

The diameter of a graph measures the maximal distance between any pair of vertices. The diameters of many small-world networks, as well as a variety of other random graph models, grow logarithmically in the number of nodes. In contrast, the worst connected networks are cycles whose diameters increase linearly in the number of nodes. In the present study we consider an intermediate class of examples: Cayley graphs of cyclic groups, also known as circulant graphs or multi-loop networks. We show that the diameter of a random circulant 2k-regular graph with n vertices scales as n^{1/k}, and establ…

随机循环图的Lovász数

The Lovász number of random circulant graphs

本文针对稠密随机循环图Lovász数行为刻画的开放问题，通过DFT对角化将其半定规划转化为线性规划，结合限制等距性质结果，证明该数期望值的标度为顶点数的平方根（相差log log因子）。

稀疏随机循环矩阵的极限谱定律

Limiting spectral laws for sparse random circulant matrices

本文研究稀疏随机循环矩阵的极限谱定律，证明其经验谱分布期望弱收敛的充要条件为群元素阶分布弱收敛，且概率收敛等价于阶分布为狄拉克质量，同时给出行列式的高概率渐近形式。