Distance Magic Labeling and Two Products of Graphs
Marcin Anholcer, Sylwia Cichacz, Iztok Peterin, Aleksandra Tepeh · Graphs and Combinatorics · 2014
Let $$G=(V,E)$$ be a graph of order $$n$$ . A distance magic labeling of $$G$$ is a bijection $$\ell :V\rightarrow \{1,\ldots ,n\}$$ for which there exists a positive integer $$k$$ such that $$\sum _{x\in N(v)}\ell (x)=k$$ for all $$v\in V $$ , where $$N(v)$$ is the neighborhood of $$v$$ . We introduce a natural subclass of distance magic graphs. For this class we show that it is closed for the direct product with regular graphs and closed as a second factor for lexicographic product with regular graphs. In addition, we characterize distance magic graphs among direct product of two cycles.