Vertex-Distinguishing E-Total Coloring of Complete Bipartite Graph $K_{7,n}$ when $7 ≤ n ≤ 95$ (Communications in Mathematical Research, 2021)
Let $G$ be a simple graph. A total coloring $f$ of $G$ is called an E-totalcoloring 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 $G$ and any vertex $x$ of $G$, let $C(x)$ denote the set of colors of vertex $x$ and of the edgesincident with , we call $C(x)$ the color set of $x$. If $C(u)≠C(v)$ for any two differentvertices $u$ and $v$ of $V (G)$, then we say that $f$ is a vertex-distinguishing E-total coloringof $G$ or a VDET coloring of $G$ for short. The minimum number of colors requiredfor a VDET coloring of $G$ is denoted by $χ^e_{vt}(G)$ and is called the VDET chromaticnumber of $G$. The VDET coloring of complete bipartite graph $K_{7,n} (7 ≤ n ≤ 95)$ isdiscussed in this paper and the VDET chromatic number of $K_{7,n} (7 ≤ n ≤ 95)$ hasbeen obtained.