TY - JOUR
T1 - Vertex-Distinguishing E-Total Coloring of Complete Bipartite Graph $K_{7,n}$ when $7 ≤ n ≤ 95$
AU - Chen , Xiang-En
JO - Communications in Mathematical Research 
VL - 4
SP - 359
EP - 374
PY - 2021
DA - 2021/05
SN - 32
DO - http://doi.org/10.13447/j.1674-5647.2016.04.08
UR - https://global-sci.org/intro/article_detail/cmr/18908.html
KW - graph, complete bipartite graph, E-total coloring, vertex-distinguishing
E-total coloring, vertex-distinguishing E-total chromatic number.
AB - <p style="text-align: justify;">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 <span style="text-align: justify;"></span><span style="text-align: justify;">$f$</span><span style="text-align: justify;"></span> of a graph $G$ and any vertex <span style="text-align: justify;"></span><span style="text-align: justify;">$x$</span><span style="text-align: justify;"></span> of $G$, let $C(x)$ denote the set of colors of vertex <span style="text-align: justify;">$x$</span> and of the edges
incident with , we call $C(x)$ the color set of $x$. If $C(u)≠C(v)$ for any two different
vertices $u$ and $v$ of $V (G)$, then we say that $f$ is a vertex-distinguishing E-total coloring
of $G$ or a VDET coloring of $G$ for short. The minimum number of colors required
for a VDET coloring of $G$ is denoted by $χ^e_{vt}(G)$ and is called the VDET chromatic
number of $G$. The VDET coloring of complete bipartite graph $K_{7,n}&nbsp;(7 ≤ n ≤ 95)$ is
discussed in this paper and the VDET chromatic number of $K_{7,n}&nbsp;(7 ≤ n ≤ 95)$ has
been obtained.</p>