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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...
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 ...