On Vertex Magic Total Labelings

Talk on Gratko seminar.

Abstract

A vertex-magic total labeling of a graph G(V,E) is defined as one-to-one mapping from V union 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. A supermagic labeling of a graph G(V,E) is defined as one-to-one mapping from E to the set of integers {1, 2,..., |E|} with the property that the sum of the labels of all edges incident to a vertex is the same constant for all vertices of the graph.

In the talk we present a technique for constructing vertex magic total labelings of Cartesian products of certain vertex magic total r-regular graphs and certain s-regular supermagic graphs with proper edge s-coloring.

If time permits we compare this technique to other methods based on decomposing G into two regular factors or/and H into two regular factors.

Talk given at

Gratko seminar at University of Minnesota Duluth, (March 24th, 2004).

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

Last update: 29.12.2011