Magic labelings of regular graphs

Talk on the conference Graphs 2005.

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 weights (sums of the label of a vertex and the labels of all edges incident to this vertex) are equal to 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 recent results on VMT and VAMT labelings of certain even-regular graphs and on VMT labelings of certain odd-regular graphs.

Talk given at

Talk given at the conference GRAFY 2005, 40th Czech and Slovak Conference of graph Theory and Combinatorics, 30th May - 3rd June 2005, Budmerice, Slovakia, (3rd June 2005).

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

Last update: 29.12.2011