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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...
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 ...
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...
The rainbow connectivity of Cayley graphs of Abelian groups
The rainbow connectivity Cayley graphs of Abelian groups
2010/11/9
A path in an edge-colored graph $G$, where adjacent edges may have the same color, is called a rainbow path if no two edges of the path are colored the same. The rainbow connectivity $rc(G)$ of $G$ i...
Two identification protocols based on Cayley graphs of Coxeter groups
Authentication Coxeter groups identification protocols random spanning trees word problem
2010/9/9
A challenge-response identification protocol is introduced, based on the intractability of the word problem in some Coxeter groups. A Prover builds his public key as the set of leaves of a tree in the...
We prove that if Cay(G; S) is a connected Cayley graph with n vertices, and the prime factorization of n is very small, then Cay(G; S) has a hamiltonian cycle. More precisely, if p, q, and r are disti...
One-regular normal Cayley graphs on dihedral groups of valency 4 or 6 with cyclic vertex stabilizer
one-regular graph Cayley graph dihedral group half-transitive graph
2007/12/10
A graph $G$ is $one$-$regular$ if its automorphism group ${\rm Aut}(G)$ acts transitively and semi-regularly on the arc set. A Cayley graph ${\rm Cay}(\Gamma,S)$ is {\it normal} if $\Gamma$ is a norma...