JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (4): 68-71.doi: 10.6040/j.issn.1671-9352.0.2015.059

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Vertex-Distinguishing E-Total coloring of complete bipartite graph K3,n with n≥18

LI Shi-ling1, CHEN Xiang-en1, WANG Zhi-wen2   

  1. 1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China;
    2. School of Mathematics and Computer Sciences, Ningxia University, Yinchuan 750021, Ningxia, China
  • Received:2015-01-30 Online:2016-04-20 Published:2016-04-08

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Abstract: Let G be a simple graph. A total coloring f of G is called an E-total coloring if no two adjacent vertices of G receive the same color, and no edge of G receives the same color as one of its endpoints. For an E-total coloring f of a graph G and any vertex x of G, let C(x)denote the set of colors of vertex x and of the edges incident with x, we call C(x)the color set of x. If C(u)≠C(v)for any two different vertices u and v of V(G), then we say that f is a vertex-distinguishing E-total coloring of G or a VDET coloring of G for short。 The minimum number of colors required for a VDET coloring of G is denoted by χevt(G)and is called the VDET chromatic number of G. The VDET coloring of complete bipartite graph K3,n is discussed in paper and the VDET chromatic number of K3,n(n≥18)has been obtained.

Key words: complete bipartite graphs, vertex-distinguishing E-total chromatic number, vertex-distinguishing E-total coloring, E-total coloring

CLC Number: 

  • O157.5
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