Distance magic labeling and two products of graphs

Abstract

Let $G=(V,E)$ be a graph of order $n$. A distance magic labeling of $G$ is a bijection $\ell :V\to 1,...,n$ 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.

References in corpus (1)

• Note on group distance magic graphs $G[C_4]$

Cited by in corpus (7)

• Spectra of Graphs and Closed Distance Magic Labelings
• Group distance magic graphs $G\times C_n$
• On distance magic circulants of valency 6
• On Distance Magic Harary Graphs
• Notes On Group Distance Magicness of Product Graphs
• Self-reverse labelings of distance magic graphs
• Distance magic labeling in complete 4-partite graphs