Distance magic labelings of product graphs
Rinovia Simanjuntak, I Wayan Palton Anuwiksa

TL;DR
This paper investigates distance magic labelings in product graphs, exploring conditions and constructions using magic rectangles for Cartesian, strong, lexicographic, and Kronecker products.
Contribution
It provides new methods for constructing distance magic labelings of product graphs using magic rectangle sets and extends existing theory to various graph products.
Findings
Distance magic labelings exist for certain product graphs.
Magic rectangle sets are effective in constructing labelings.
Results extend the understanding of labelings in complex graph products.
Abstract
A graph is said to be distance magic if there exists a bijection and a constant {\sf k} such that for any vertex , , where is the set of all neighbours of . 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.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · graph theory and CDMA systems
