Description
In this talk we will present various kinds of graph labelings where the labels are members of Abelian groups. The talk will consist of two parts. In the first part we will present the reults on the so-called irregular labelings, i.e. such labelings of edges with elements of arbitrary Abelian groups that resulting sums at vertices are dstinct either for all the vertices of the graph or for the neigbouring vertices only. The minimum size of an Abelian group that allows such a labeling is called group irregularity strength or group sum chromatic number, respectively. We will give exact formulae or bounds for both graph invariants for arbitrary graphs. In the second part of the talk we will try to find a bijection from the set of vertices to an arbitrary Abelian group of order $n$ (where $n$ is the number of vertices) such that for each vertex the sum of the labels of its neighbors is the same. Such labelings are called group distance magic labelings. We will discuss the existence of such labelings for chosen families of graphs, in particular for direct products of graphs.
Primary author
Dr
Marcin Anholcer
(Poznań University of Economics)
