The modified bubble-sort graph of dimension n is the Cayley graph of Sn generated by n cyclically adjacent transpositions. In the present paper, it is shown that the automorphism group of the modified bubble sort graph of dimension n is Sn × D2n, for all n ≥ 5. Thus, a complete structural description of the automorphism group of the modified bubble-sort graph is obtained. A similar direct produ...

An embedding of a simple graph G into its complement G is a permutation σ on V (G) such that if an edge xy belongs to E(G), then σ(x)σ(y) does not belong to E(G). In this note we consider some families of embeddable graphs such that the corresponding permutation is cyclic.

We start by studying the distribution of (cyclically reduced) elements of the free groups Fn with respect to their abelianization (or equivalently, their class in H1(Fn,Z)). We derive an explicit generating function, and a limiting distribution, by means of certain results (of independent interest) on Chebyshev polynomials; we also prove that the reductions mod p (p – an arbitrary prime) of the...

In a recent paper Carot et al. considered the definition of cylindrical symmetry as a specialisation of the case of axial symmetry. One of their propositions states that if there is a second Killing vector, which together with the one generating the axial symmetry, forms the basis of a two-dimensional Lie algebra, then the two Killing vectors must commute, thus generating an Abelian group. In t...

Graph G is called cyclically orientable (CO) if it admits an orientation in which every simple chordless cycle is cyclically oriented. This family of graphs was introduced by Barot, Geiss, and Zelevinsky in their paper “Cluster algebras of finite type and positive symmetrizable matrices”, J. London Math. Soc. 73 Part 3 (2006), 545-564. The authors obtained several nice characterizations of CO-g...

A sequence is called perfect if its autocorrelation function is a delta function. In this paper, we give a new definition of autocorrelation function: generalized even and odd periodic autocorrelation, and generalized even and odd periodic cyclically conjugated autocorrelation. In particular, we study a special case of autocorrelation function called cyclically conjugated autocorrelation functi...

A cascaded GMW function, which deenes a cascaded GMW sequence, is a composition of a nite number of trace functions and exponential functions over nite elds, and is determined by a parameter system. Two such functions are said to be cyclically equivalent if the sequences deened by them are cyclically equivalent. In this paper, the problem how to decompose any given cascaded GMW function by trac...

A method for analysis of essentially nonlinear vibrations of cyclically symmetric structure has been developed. Two major cases are analysed: (i) steady-state periodic multiharmonic vibrations; (ii) transient vibrations. The method allows exact calculation of the essentially nonlinear vibrations to be performed using a model for only one period of the cyclic symmetry. A rigorously proof of poss...