Acta Scientiarum Naturalium Universitatis Sunyatseni ›› 2020, Vol. 59 ›› Issue (4): 134-143.doi: 10.13471/j.cnki.acta.snus.2019.06.12.2019A047

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Vertex-distinguishing IE-total coloring of K4,4,p (4≤ p ≤1 007) 

MA Jingjing, CHEN Xiang'en   

  1. College of Mathematics and StatisticsNorthwest Normal UniversityLanzhou 730070China
  • Received:2019-06-12 Online:2020-07-25 Published:2020-07-25

Abstract: Let G be a simple graph.An IE-total coloring f of G is called that if there are no two adjacent vertices of G receive the same color, For an IE-total coloring f of G, if C(u)≠C(v) for two distinct vertex  u and v, where Cf (x) or 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-distingushing IE-total coloring of G. By using of themethods of distributing the color sets in advance, constructing the colorings and contradiction, the vertex-distinguishing IE-total coloring of complete tripartite graphs K4,4,p (4≤ p≤1 007) is discussed. The vertex-distinguishing IE-total chromatic number of K4,4,p(4≤ p ≤1 007) is determined.

Key words: complete tripartite graph,  , IE-total coloring,  , vertex-distinguishing IE-total coloring

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