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Adjacent vertex distinguishing edge colorings of the direct product of a regular graph by a path or a cycle. (English) Zbl 1229.05103

Summary: We investigate the minimum number of colors required for a proper edge coloring of a finite, undirected, regular graph \(G\) in which no two adjacent vertices are incident to edges colored with the same set of colors. In particular, we study this parameter in relation to the direct product of \(G\) by a path or a cycle.

MSC:

05C15 Coloring of graphs and hypergraphs
05C38 Paths and cycles
05C76 Graph operations (line graphs, products, etc.)
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