Distance magic labelings of product graphs

Abstract

A graph $G$ is said to be distance magic if there exists a bijection $f:V\to \{1,2,\dots ,v\}$ and a constant {\sf k} such that for any vertex $x$, ${\sum }_{y\in N(x)}f(y)=\mathsf{k}$, where $N_{(}x)$ is the set of all neighbours of $x$. In this paper we shall study distance magic labelings of graphs obtained from four graph products: cartesian, strong, lexicographic, and cronecker. We shall utilise magic rectangle sets and magic column rectangles to construct the labelings.

21 pages, the Second Malta Conference in Graph Theory and Combinatorics