Vertex-Distinguishing IE-Total Colorings of Complete Bipartite Graphs Km,N(m < n)

Xiang’en Chen, Yuping Gao, and Bing Yao. "Vertex-Distinguishing IE-Total Colorings of Complete Bipartite Graphs Km,N(m < n)." Discussiones Mathematicae Graph Theory 33.2 (2013): 289-306. <http://eudml.org/doc/267543>.

@article{Xiang2013,
abstract = {Let G be a simple graph. An IE-total coloring f of G is 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) 6= C(v) for any two different vertices u and v of 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 χie vt(G), and is called vertex-distinguishing IE-total chromatic number or the VDIET chromatic number of G for short. VDIET colorings of complete bipartite graphs Km,n(m < n) are discussed in this paper. Particularly, the VDIET chromatic numbers of Km,n(1 ≤ m ≤ 7,m < n) as well as complete graphs Kn are obtained.},
author = {Xiang’en Chen, Yuping Gao, Bing Yao},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {complete bipartite graphs; IE-total coloring; vertex-distinguishing IE-total coloring; vertex-distinguishing IE-total chromatic number},
language = {eng},
number = {2},
pages = {289-306},
title = {Vertex-Distinguishing IE-Total Colorings of Complete Bipartite Graphs Km,N(m < n)},
url = {http://eudml.org/doc/267543},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Xiang’en Chen
AU - Yuping Gao
AU - Bing Yao
TI - Vertex-Distinguishing IE-Total Colorings of Complete Bipartite Graphs Km,N(m < n)
JO - Discussiones Mathematicae Graph Theory
PY - 2013
VL - 33
IS - 2
SP - 289
EP - 306
AB - Let G be a simple graph. An IE-total coloring f of G is 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) 6= C(v) for any two different vertices u and v of 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 χie vt(G), and is called vertex-distinguishing IE-total chromatic number or the VDIET chromatic number of G for short. VDIET colorings of complete bipartite graphs Km,n(m < n) are discussed in this paper. Particularly, the VDIET chromatic numbers of Km,n(1 ≤ m ≤ 7,m < n) as well as complete graphs Kn are obtained.
LA - eng
KW - complete bipartite graphs; IE-total coloring; vertex-distinguishing IE-total coloring; vertex-distinguishing IE-total chromatic number
UR - http://eudml.org/doc/267543
ER -