Distinguishing colorings of graphs and their subgraphs

Abstract

In this paper, several distinguishing colorings of graphs are studied, such as vertex distinguishing proper edge coloring, adjacent vertex distinguishing proper edge coloring, vertex distinguishing proper total coloring, adjacent vertex distinguishing proper total coloring. Finally, some related chromatic numbers are determined, especially the comparison of the correlation chromatic numbers between the original graph and the subgraphs are obtained.

Keywords

• vertex distinguishing edge coloring
• adjacent vertex distinguishing edge coloring
• vertex distinguishing total coloring
• adjacent vertex distinguishing total coloring