Abstract:

The vertex-distinguishing edge colorings of the lexicographic product of some special graphs are studied, such as the lexicographic product of a wheel (or fan, star) and a complete graph, the lexicographic product of a wheel (or fan, star) and a complete bipartite graph etc. The vertex-distinguishing edge chromatic numbers of the Mycielski′s graphs of these lexicographic product graphs are obtained by constructing edge-colorings.

Key words: lexicographic product; Mycielski′s graph; vertex-distinguishing edge coloring; vertex-distinguishing edge chromatic number