Abstract:

Let G be a simple graph. An IEtotal coloring f of G refers to a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color. Let C(u) be the set of colors of vertex u and edges incident to u under f. For an IEtotal coloring f of G using k colors, if C(u)≠C(v) for any two different vertices u and v of V(G), then f is called a kvertexdistinguishing IEtotalcoloring of G, or a kVDIET coloring of G for short. The minimum number of colors required for a VDIET coloring of G is denoted by χievt (G), and it is called the VDIET chromatic number of G. VDIET chromatic numbers for the complete bipartite graph K5,n (n≥6) were given.

Key words: graphs; vertexdistinguishing IEtotal coloring; vertexdistinguishing IEtotal chromatic number; complete bipartite graph