$\parbox{7cm}{ {\Huge\bf SEMINARIUM}}$
Matematyka Dyskretna
(prowadzone przez M.Woźniaka)

We wtorek, 26 kwietnia 2005 roku, o godzinie 12:45

w sali 304, łącznik A-3-A-4, A G H

Petr KOVÁR

(VŠB - Technical University of Ostrava)

wygłosi referat pod tytułem:

Magic labelings of regular graphs

A vertex magic total (VMT) labeling of a graph $G(V,E)$ is defined as one-to-one mapping from $V\cup E$ to the set of integers $\{1, 2,..., \vert V\vert+\vert E\vert\}$ 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 $V\cup E$ to the set of integers $\{1, 2,..., \vert V\vert+\vert E\vert\}$ 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 $K_2$ and $2K_3$ 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.

Serdecznie zapraszamy wszystkich chętnych!