### Vertex-distinguishing E-total coloring of complete bipartite graph K10,n with 10≤n≤90

1. 1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China;
2. College of Mathematics and Statistics, Ningxia University, Yinchuan 750021, Ningxia, China
• Online:2018-12-20 Published:2018-12-18

Abstract: Let G be a simple graph. An E-total coloring f of G is called that if there are no two adjacent vertices of G receive the same color, and no edges of G receives the same color as one of its endpoints. For an E-total coloring f of G, if C(u)≠C(v) for any two distinct vertices u and v of V(G), where C(x) denotes the set of colors of vertex x and of the edges incident with x under f, then f is called a vertex-distinguishing E-total coloring of G. Let χevt(G)=min{k|G has a k-VDET coloring}. Then χevt(G) is called the VDET chromatic number of G. By using analytical method and proof by contradiction, the VDET coloring of complete bipartite graph K10,n is discussed and the VDET chromatic number of K10,n(10≤n≤90) has been obtained.

CLC Number:

• O157.5
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