This paper provides further results on the perfect state transfer in integral circulant graphs (ICG graphs). The non-existence of PST is proved for several classes of ICG graphs containing an isolated divisor d0, i.e. the divisor which is relatively prime to all other divisors from d ∈ D \ {d0}. The same result is obtained for classes of integral circulant graphs having the NSF property (i.e. e...

Let (bn) = (b1, b2, . . . ) be a sequence of integers. A primitive prime divisor of a term bk is a prime which divides bk but does not divide any of the previous terms of the sequence. A zero orbit of a polynomial φ(z) is a sequence of integers (cn) where the n-th term is the n-th iterate of φ at 0. We consider primitive prime divisors of zero orbits of polynomials. In this note, we show that f...

For a commutative semigroup S with 0, the zero-divisor graph of S denoted by Γ(S) is the graph whose vertices are nonzero zero-divisor of S, and two vertices x, y are adjacent in case xy = 0 in S. In this paper we study the case where the graph Γ(S) is complete r-partite for a positive integer r. Also we study the commutative semigroups which are finitely colorable.

Tree series transformations computed by polynomial topdown and bottom-up tree series transducers are considered. The hierarchy of tree series transformations obtained in [Fülöp, Gazdag, Vogler: Hierarchies of Tree Series Transformations. Theoret. Comput. Sci. 314(3), p. 387–429, 2004] for commutative izz-semirings (izz abbreviates idempotent, zero-sum and zero-divisor free) is generalized to ar...

Let F/Fq be an algebraic function field of genus g defined over a finite field Fq. We obtain new results on the existence, the number and the density of dimension zero divisors of degree g− k in F/Fq where k is an integer ≥ 1. In particular, for q = 2, 3 we prove that there always exists a dimension zero divisor of degree γ − 1 where γ is the q-rank of F and in particular a non-special divisor ...

For n ∈ N and D ⊆ N, the distance graph P n has vertex set {0, 1, . . . , n− 1} and edge set {ij | 0 ≤ i, j ≤ n − 1, |j − i| ∈ D}. Note that the important and very well-studied circulant graphs coincide with the regular distance graphs. A fundamental result concerning circulant graphs is that for these graphs, a simple greatest common divisor condition, their connectivity, and the existence of ...