Vertex-distinguishing IE-total Colorings of Cycles and Wheels
Chen, Xiang-en, Chen Xiang-en, Wenyu, Li, Ze-Peng, Yao · 2014
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 x_(vt)~(ie)(G),and is called the VDIET chromatic number of G.We get the VDIET chromatic numbers of cycles and wheels,and propose related conjectures in this paper.