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

Xiang’en Chen; Yuping Gao; Bing Yao

Discussiones Mathematicae Graph Theory (2013)

- Volume: 33, Issue: 2, page 289-306
- ISSN: 2083-5892

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topXiang’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 -

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