Remarks on Vertex-Distinguishing IE-Total Coloring of Complete Bipartite Graphs K4,n and Kn,n |
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Authors: | Xiang'en CHEN Xiaoqing XIN Wenyu HE |
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Affiliation: | College of Mathematics and Information Science, Northwest Normal University,Gansu 730070, P. R. China |
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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 χ ie vt (G),and it is called the VDIET chromatic number of G.We will give VDIET chromatic numbers for complete bipartite graph K4,n (n≥4),K n,n (5≤ n ≤ 21) in this article. |
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Keywords: | graphs IF-total coloring vertex-distinguishing IE-total coloring vertex-distinguishing IE-total chromatic number complete bipartite graph |
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