Upper Bounds for the D(1)-Vertex-Distinguishing EI-Total Chromatic Numbers of Graphs
Xinsheng Liu, Zhiqiang Wang · ASME Press eBooks · 2011
Let G(V,E) be a simple connected graph, and |V(G)| 1Â¥ 2. Suppose k, 1 are both positive integers and f is a mapping from V(G)1ªE(G) to {1, 2, 1¦, k}, such that 1) uv1ˆE(G)(u 1 v), f(u) 1 f(v); 2) uv1ˆE(G)(u 1 v), dG(u,v) ≤ 1, where dG(u,v) denotes the distance between u and v, we have C(u) 1 C(v), where C(u) = {f(u)}1ª{f(uv)|uv1ˆE(G)}. Then f is called a k-D(1)-vertex-distinguishing EI-total coloring of G. In this paper we study the upper bounds for the D(1)-vertex-distinguishing EI-total chromatic numbers by the probability method and prove that 11vtei(G) ≤ 321(1+2)/1 when 1 1Â¥ 5, 1 1Â¥ 4.