Distance Magic Cartesian Products of Graphs

• Autorzy: Sylwia Cichacz , Dalibor Froncek , Elliot Krop , Christopher Raridan
• Języki publikacji: EN

Abstrakty

EN

A distance magic labeling of a graph G = (V,E) with |V | = n is a bijection ℓ : V → {1, . . . , n} such that the weight of every vertex v, computed as the sum of the labels on the vertices in the open neighborhood of v, is a constant. In this paper, we show that hypercubes with dimension divisible by four are not distance magic. We also provide some positive results by proving necessary and sufficient conditions for the Cartesian product of certain complete multipartite graphs and the cycle on four vertices to be distance magic.

Słowa kluczowe

EN

distance magic labeling; magic constant; sigma labeling; Cartesian product; hypercube; complete multipartite graph; cycle

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2016
• Tom: 36
• Numer: 2
• Strony: 299-308

Daty

wydano

2016-05-01

otrzymano

2014-09-01

poprawiono

2015-06-19

zaakceptowano

2015-06-19

online

2016-04-15

Twórcy

autor

Sylwia Cichacz

• AGH University of Science and Technology Kraków, Poland

autor

Dalibor Froncek

• Department of Mathematics and Statistics University of Minnesota-Duluth, USA

autor

Elliot Krop

• Department of Mathematics Clayton State University, USA

autor

Christopher Raridan

• Department of Mathematics Clayton State University, USA

Identyfikatory

DOI

10.7151/dmgt.1852