Vertex-Distinguishing Total Coloring of Ladder Graphs (<i>N</i>=0(mod 8) )

Abstract

A proper total coloring of a simple graph G is called vertex distinguishing if for any two distinct vertices u and v in G, the set of colors assigned to the elements incident to u differs from the set of colors incident to v. The minimal number of colors required for a vertex distinguishing total coloring of G is called the vertex distinguishing total coloring chromatic number. In a paper, we give a “triangle compositor”, by the compositor, we proved that when n=0(mod 8) and , vertex distinguishing total chromatic number of “ladder graphs” is n.