Year: 2016
Author: Xiang-En Chen
Communications in Mathematical Research , Vol. 32 (2016), Iss. 4 : pp. 359–374
Abstract
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 $G$ and any vertex $x$ of $G$, let $C(x)$ denote the set of colors of vertex $x$ 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 $K_{7,n} (7 ≤ n ≤ 95)$ is discussed in this paper and the VDET chromatic number of $K_{7,n} (7 ≤ n ≤ 95)$ has been obtained.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2016.04.08
Communications in Mathematical Research , Vol. 32 (2016), Iss. 4 : pp. 359–374
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: graph complete bipartite graph E-total coloring vertex-distinguishing E-total coloring vertex-distinguishing E-total chromatic number.