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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Symmetry in Cayley graphs
凯莱图 对称性 图论
2023/4/27
Cayley graphs form an important class of vertex-transitive graphs, which have been the object of study for many decades. These graphs admit a group of automorphisms that acts regularly (sharply-transi...
We show that for integers k > 1 and n > 2, the diameter of the Cayley graph of SLn(Z/kZ) with respect to a standard two-element generating set, is at most a constant times n2 ln k. This answers a ques...
We give a non-deterministic algorithm that expresses elements of SLN(Z), for N>2, as words in a finite set of generators, with the length of these words at most a constant times the word metric. We sh...
There are many interesting questions one can ask about a highly symmetric graph.
A graph with a transitive automorphism group can be obtained starting with a group
G and a small set S of generators....
对称群上Cayley图的条件匹配排除数
完美匹配 Cayley图 条件匹配排除
2013/12/4
一个图的条件匹配排除数是最少的边的数量,使得从图中删除这些边后形成的图既没有孤立点,也没有完美匹配和几乎完美匹配. 条件匹配排除数是衡量网络在边故障情况下的鲁棒性的参数之一.本文给出了对称群上Cayley图的条件匹配排除数.
Determination of Integral Cayley Graphs on Finite Abelian Groups
abelian group character cayley graph integral graph
2012/6/21
A graph is integral means that all its eigenvalues are integers. In this note, we determine all the integral Cayley graphs on finite abelian groups. Moreover, we calculate the the number of integral C...
Odd-order Cayley graphs with commutator subgroup of order pq are hamiltonian
Cayley graph hamiltonian cycle commutator subgroup
2012/5/9
We show that if G is a nontrivial, finite group of odd order, whose commutator subgroup [G,G] is cyclic of order p^m q^n, where p and q are prime, then every connected Cayley graph on G has a hamilton...
Strongly Regular Cayley Graphs, Skew Hadamard Difference Sets, and Rationality of Relative Gauss Sums
strongly regular graph skew Hadamard difference set relative Gauss sum
2012/3/1
In this paper, we give constructions of strongly regular Cayley graphs and skew Hadamard difference sets. Both constructions are based on choosing cyclotomic classes in finite fields, and our results ...
On $p$-adic Gibbs Measures for Hard Core Model on a Cayley Tree
Cayley trees hard core interaction Gibbs measures translation invariant measures periodic measures
2011/9/20
Abstract: In this paper we consider a nearest-neighbor $p$-adic hard core (HC) model, with fugacity $\lambda$, on a homogeneous Cayley tree of order $k$ (with $k + 1$ neighbors). We focus on $p$-adic ...
Cayley-Dickson and Clifford Algebras as Twisted Group Algebras
twisted group algebra sign function Cayley-Dickson algebra Clifford algebra quaternions octonions
2011/8/26
Abstract: The effect of some properties of twisted groups on the associated algebras, particularly Cayley-Dickson and Clifford algebras. It is conjectured that the Hilbert space of square-summable seq...
A catalog of Cayley-Dickson-like products
twisted group algebra Cayley-Dickson algebra quaternions octonions Fano plane
2011/8/26
Abstract: A catalog of all 32 Cayley-Dickson-like doubling products on ordered pairs (a,b),(c,d) for which (1,0) is the left and right identity and for which xx* and x*x equal the square of the norm o...
Combinatorial R-trees as generalized Cayley graphs for fundamental groups of one-dimensional spaces
R-tree generalized Cayley graph one-dimensional space
2011/8/29
Abstract: In their study of fundamental groups of one-dimensional path-connected compact metric spaces, Cannon and Conner have asked: Is there a tree-like object that might be considered the topologic...
Uniform existence of the integrated density of states on metric Cayley graphs
random Schrodinger operator metric graph quantum graph integrated density of states
2011/7/27
Abstract: Given a finitely generated amenable group we consider ergodic random Schr\"odinger operators on a Cayley graph with random potentials and random boundary conditions. We show that the normali...
基于Cayley变换的紧支撑二元正交小波滤波器组的构造
正交小波滤波器组 仿酉矩阵 Cayley变换
2012/8/2
构造正交滤波器组, 在多相域里就等价于构造仿酉矩阵, 而仿酉矩阵的构造涉及到非线性方程组的求解.通过对Cayley变换的研究, 把仿酉矩阵的构造转换为更易构造的仿斜厄米特矩阵, 基于这种变换构造了二元紧支撑正交小波滤波器组, 并给出了算例.
A group has a planar Cayley complex if and only if it has a VAP-free Cayley graph
planar Cayley complex VAP-free Cayley graph
2010/11/23
We prove that a group has a planar Cayley complex if and only if it has a Cayley graph that can be embedded in the euclidean plane without accumulation points of vertices.