Magic Labelings of Regular Graphs

Talk on SEMINARIUM Matematyka Dyskretna.

Abstract

A vertex-magic total (VMT) labeling of a graph G(V,E) is defined as one-to-one mapping from V ∪ E to the set of integers {1, 2, ..., |V|+|E|} with the property that the sum of the label of a vertex and the labels of all edges incident to this vertex is the same constant for all vertices of the graph. An (s,d)-vertex antimagic total (VAMT) labeling of a graph G(V,E) is defined as one-to-one mapping from V ∪ E to the set of integers {1, 2, ..., |V|+|E|} with the property that the weights form an arithmetic progression starting at s with difference d.

J. MacDougall conjectured that any regular graph with the exception of K₂ and 2K₃ has a VMT labeling.

In the talk we present a technique for constructing VMT and VAMT labelings of certain regular graphs based on decomposing G into 2-regular factors and on Kotzig arrays.

Talk given at

Talk given at the SEMINARIUM Matematyka Dyskretna, AVG, Krakow, 26th April 2005.

Petr<dot>Kovar<at>vsb<dot>cz phone ++420 / 597 325 972

Last update: 29.12.2011