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

• Autorzy: Xiang’en Chen , Yuping Gao , Bing Yao
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

complete bipartite graphs; IE-total coloring; vertex-distinguishing IE-total coloring; vertex-distinguishing IE-total chromatic number

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2013
• Tom: 33
• Numer: 2
• Strony: 289-306

Daty

wydano

2013-05-01

online

2013-04-13

Twórcy

autor

Xiang’en Chen

• College of Mathematics and Information Science Northwest Normal University, Lanzhou 730070, P. R. China

autor

Yuping Gao

• College of Mathematics and Information Science Northwest Normal University, Lanzhou 730070, P. R. China

autor

Bing Yao

• College of Mathematics and Information Science Northwest Normal University, Lanzhou 730070, P. R. China

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1659