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• # Artykuł - szczegóły

## Discussiones Mathematicae Graph Theory

2013 | 33 | 2 | 289-306

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

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.

EN

289-306

wydano
2013-05-01
online
2013-04-13

### Twórcy

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

### Bibliografia

• [1] P.N. Balister, B. Bollobás and R.H. Shelp, Vertex distinguishing colorings of graphs with Δ(G) = 2, Discrete Math. 252 (2002) 17-29. doi:10.1016/S0012-365X(01)00287-4[Crossref]
• [2] P.N. Balister, O.M. Riordan and R.H. Schelp, Vertex distinguishing edge colorings of graphs, J. Graph Theory 42 (2003) 95-109. doi:10.1002/jgt.10076[Crossref]
• [3] C. Bazgan, A. Harkat-Benhamdine, H. Li and M. Wo´zniak, On the vertexdistinguishing proper edge-colorings of graphs, J. Combin. Theory (B) 75 (1999) 288-301. doi:10.1006/jctb.1998.1884[Crossref]
• [4] A.C. Burris and R.H. Schelp, Vertex-distinguishing proper edge-colorings, J. Graph Theory 26 (1997) 73-82. doi:10.1002/(SICI)1097-0118(199710)26:2h73::AID-JGT2i3.0.CO;2-C[Crossref]
• [5] J. Černý, M. Horňák and R. Soták, Observability of a graph, Math. Slovaca 46 (1996) 21-31.
• [6] X. Chen, Asymptotic behaviour of the vertex-distinguishing total chromatic numbers of n-cube, J. Northwest Univ. 41(5) (2005) 1-3.
• [7] F. Harary and M. Plantholt, The point-distinguishing chromatic index, in: F. Harary, J.S. Maybee (Eds.), Graphs and Application, New York (1985) 147-162.
• [8] M. Horňák and R. Soták, Observability of complete multipartite graphs with equipotent parts, Ars Combin. 41 (1995) 289-301.
• [9] M. Horňák and R. Soták, Asymptotic behaviour of the observability of Qn, Discrete Math. 176 (1997) 139-148. doi:10.1016/S0012-365X(96)00292-0[Crossref]
• [10] M. Horňák and R. Soták, The fifth jump of the point-distinguishing chromatic index of Kn,n, Ars Combin. 42 (1996) 233-242.
• [11] M. Horňák and R. Soták, Localization jumps of the point-distinguishing chromatic index of Kn,n, Discuss. Math. Graph Theory 17 (1997) 243-251. doi:10.7151/dmgt.1051[Crossref]
• [12] M. Horňák and N. Zagaglia Salvi, On the point-distinguishing chromatic index of complete bipartite graphs, Ars Combin. 80 (2006) 75-85.
• [13] N. Zagaglia Salvi, On the point-distinguishing chromatic index of Kn,n, Ars Combin. 25B (1988) 93-104.
• [14] N. Zagaglia Salvi, On the value of the point-distinguishing chromatic index of Kn,n, Ars Combin. 29B (1990) 235-244.
• [15] Z. Zhang, P. Qiu, B. Xu, J. Li, X.Chen and B.Yao, Vertex-distinguishing total colorings of graphs, Ars Combin. 87 (2008) 33-45.