Year: 2014
Author: Xiang-En Chen, Wenyu He, Zepeng Li, Bing Yao
Communications in Mathematical Research , Vol. 30 (2014), Iss. 3 : pp. 222–236
Abstract
Let $G$ be a simple graph. An IE-total coloring $f$ of $G$ refers to a coloring of the vertices and edges of $G$ so that no two adjacent vertices receive the same color. Let $C(u)$ be the set of colors of vertex $u$ and edges incident to $u$ under $f$. For an IE-total coloring $f$ of $G$ using $k$ colors, if $C(u)≠C(v)$ for any two different vertices $u$ and $v$ of $V (G)$, then $f$ is called a $k$-vertex-distinguishing IE-total-coloring of $G$, or a $k$-VDIET coloring of $G$ for short. The minimum number of colors required for a VDIET coloring of $G$ is denoted by $χ^{ie}_{vt}(G)$, and is called the VDIET chromatic number of $G$. We get the VDIET chromatic numbers of cycles and wheels, and propose related conjectures in this paper.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2014.03.04
Communications in Mathematical Research , Vol. 30 (2014), Iss. 3 : pp. 222–236
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: graph IE-total coloring vertex-distinguishing IE-total coloring vertex-distinguishing IE-total chromatic number.