关键词: 图, 点可区别V-全染色, 点可区别V-全色数

Abstract: For vertex distinguishing V-total coloring of graph [G], the colors of both adjacent edges and vertex with its incident edges should be different. Moreover, the color sets of any vertices are not the same. The minimum coloring number is called the vertex-distinguishing V-total chromatic number of [G]. This paper presents a heuristic algorithm for vertex distinguishing V-total coloring according to its constrain rules. The algorithm iterates gradually in proper sequence with the help of the color matrix and complementary set. When the generic function value meets the requirement, we say that the current coloring is successful. This paper gives a detail description of the algorithm, algorithm analysis and algorithm testing results, and also verifies the vertex distinguishing V-total coloring conjecture of graphs with given points. The experimental results show that the algorithm has good efficiency and can obtain the vertex distinguishing V-total chromatic number of graphs, and the time complexity of the algorithm is not more than[O(n3)].

Key words: graphs, vertex-distinguishing V-total coloring, vertex-distinguishing V-total chromatic number