Distance magic (r, t)-hypercycles
PBN-AR
Instytucja
Wydział Matematyki Stosowanej (Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie)
##### Informacje podstawowe
Główny język publikacji
EN
Czasopismo
Utilitas Mathematica
ISSN
0315-3681
EISSN
Wydawca
Winnipeg, Man.: Utilitas Mathematica Publ.
URL
Rok publikacji
2016
Numer zeszytu
Strony od-do
283--294
Numer tomu
101
Liczba arkuszy
0.8
##### Autorzy
(liczba autorów: 1)  Sylwia Cichacz-Przeniosło
##### Słowa kluczowe
EN
distance magic labeling
hypercycles
powers of cycles
##### Streszczenia
Język
EN
Treść
A hypergraph H is a pair H = (V, E) where V is a set of vertices and E is a set of non-empty subsets of V called hyperedges. If all edges have the same cardinality t, the hyper-graph is said to be t-uniform. Let H = (V, E) be a hyper graph of order n. A distance magic labeling of H is a bijection l: V -> {1, 2,...,n} for that there exists a positive integer k such that Sigma(x is an element of N(v)) l(x) = k for all v is an element of V, where N(v) is the open neighborhood of v. The (r, t)-hypercycle, 1 <= r <= t - 1, is defined as t-uniform hypergraph whose vertices can be ordered cyclically in such a way that the edges are segments of that cyclic order and every two consecutive edges share exactly r vertices. It was proved that (1, 2)-hypercycle of order n is a distance magic graph if and only if n = 4 (). In this paper we prove that if p is odd, then the p-th power of a cycle C-n is a distance magic graph if and only if 2p(p +1) 0 (mod n), n >= 2p + 2 and n/gcd(n,p+1) equivalent to 0 (mod 2). Using this fact we we solve the problem of distance magic (r, t)-hypercycles for t = 3, 4, 6.
original article
peer-reviewed
##### Inne
System-identifier
idp:102698