%A CHEN Xiang’en, YANG Weiguang
%T Vertex-distinguishing E-total coloring of a complete bipartite graph *K*_{9, n} (93 ≤ *n* ≤ 216)
%0 Journal Article
%D 2020
%J Journal of East China Normal University(Natural Science)
%R 10.3969/j.issn.1000-5641.201911028
%P 24-29
%V 2020
%N 6
%U {https://xblk.ecnu.edu.cn/CN/abstract/article_25780.shtml}
%8
%X Let $G$ be a simple graph. A total coloring $f$ of $G$ is called an E-total coloring if no two adjacent vertices of $G$ receive the same color, and no edge of $G$ receives the same color as one of its endpoints. For an E-total coloring $f$ of a graph $G$, if $C(u)\neq C(v)$ for any two distinct vertices $u$ and $v$ of $V(G)$, where $C(x)$ denotes the set of colors of vertex $x$ and of the edges incident with $x$ under $f$, then $f$ is called a vertex-distinguishing E-total coloring of $G$. Let $\chi _{vt}^{e}(G)=\min\{k: G$ has a $k$-VDET coloring$\}.$ Then, $\chi _{vt}^{e}(G)$ is called the VDET chromatic number of $G$. By using contradiction, the method of a combinatorial analysis and the method of constructing specific coloring, the VDET coloring of a complete bipartite graph $K_{9, n}$ is discussed and the VDET chromatic number of $K_{9, n}\; (93\leqslant n\leqslant 216)$ is determined.