摘要对于图G(V，E)，若存在正整数k(1≤k≤|G|＋|E|)和映射f：V(G)∪Ε(G)→{1,2，…，k}，使得对任意两点u，v∈V(G)，有S(u)＝S(v)，其中S(u)＝f(u)＋∑Gf(uw)，则称f为G的点魔幻全染色，且称χVMTC(G)＝max{k|k－VMTC of G}为点魔幻全色数.在已有的点魔幻标号和点可区别染色研究基础之上，结合实际问题提出了点魔幻全染色(VMTC)，设计了一种新型的点魔幻全染色算法，该算法使用迭代寻优的方式对随机图进行了研究，通过实验结果分析，总结得到了若干定理并给出证明.
Abstract：For graph G(V，E)，if there is a positive integer k(1≤k≤|G|＋|E|) and a mapping f：V(G)∪E(G)→{1,2，…，k}，so that for any two points u，v∈V(G)，there is S(u)＝S(v)，where S(u)＝f(u)＋∑Gf(uw)， then f is called the vertex magic total coloring of G，and χvmtc(G)＝max{k|k－VMTC of G} is called the vertex magic panchromatic number. Based on the existing research on vertex magic labeling and vertex distinguishing coloring， combined with practical problems， vertex magic total coloring is proposed， and a new vertex magic total coloring algorithm is designed. The algorithm uses iterative optimization to study the random graph. Through the analysis of experimental results， several theorems and proofs are obtained.
2023, Vol. 57 
