The Algorithm Research on the Strong Vertex-Distinguishing Total Coloring of Complete Graph

Let G(V,E) be a simple connect graph with order not less than 3,k is an natural number and f is a mapping from V(G)boolean OR E(G) to {1,2 ... ,k}, if for any uv is an element of E(G), we have f(u) not equal f(v),f(u) not equal f(uv) ,f(v) not equal f(uv); for any uv, uw is an element of E(G),(v not equal w),f(uv) not equal f(uw); for any u,v is an element of V(G)C(u) not equal C(v), while C(u)={f(u)}boolean OR{f(w)\uw is an element of E(G)} boolean OR{f(uw)\uw is an element of E(G)}, C(v)={f(v)} boolean OR {f(e)\ve is an element of E(G)} boolean OR {f(ve)\ve is an element of E(G)}. Then f is called strong vertex-distinguishing total coloring of graph G(k-VSDTC of G if brief) and the number chi(vst)(G) = min k\ the all k - VSDTCof G} is called the strong vertex-distinguishing total chromatic number of G. In this paper, we design and implement an algorithm. It proves and gets the given point of complete graph of strong vertex-distinguishing total chromatic number.