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)¡ÈE(G) to {1,2¡···,k}.if for any uv¡ÊE(G), we have f(u) ¡Ùf(v),f(u) ¡Ùf(uv), f(v) ¡Ùf(uv); for any uv, uw¡ÊE(G),(v¡Ùw),f(uv) ¡Ùf(uw);for any u, v¡ÊV(G)C(u)¡ÙC(v), while C(u)={f(u)}¡È{f(w)|uw¡ÊE(G)} ¡È{f(uw)|uw¡ÊE(G)}, C(v)={f(v)}¡È{f(e)|ve¡ÊE(G)} ¡È{f(ve)|ve¡ÊE(G)}.Then f is called strong vertex-distinguishing total coloring of graph G(k-VSDTC of G if brief) and the number 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.