DOI: 10.36347/sjpms.2020.v07i01.001

Pages: 1-6

With the wide application of graph coloring in real life,it has gradually become one of the important fields studied by many scholars. A general total coloring of graph G refers to mapping f : V(G) E(G) 1,k.For any xV(G),let Cf (x) or C(x) be the set of colors of vertex x and edges incident with x under f, which is called the color set of point x under f. For any u,vV(G), if C(u)C(v), then f is called a k-vertex distinguishing general-total coloring of graph G (kGVDTC).The minimum number of colors required for a VDIETC of G is denoted by gvt(G), which is called the vertex distinguishing general-total chromatic number of graph G. Vertex distinguishing general-total coloring of complete tripartite graph K2,5,p is discussed in this paper by using the methods of distributing the color sets in advance, constructing the colorings and contradiction. The vertex distinguishing general-total chromatic numbers of K2,5,p are determined.