Δ(G)≤3的2-连通外平面图的Smarandachely 邻点可区别全色数

Smarandachely Adjacent Vertex-Distinguishing Total Coloring of 2-Connected Outerplanar Graphs with Δ(G)≤3

Smrandachely邻点可区别全染色是相邻点的色集合互不包含的邻点可区别全染色,是对邻点可区别全染色的条件的进一步加强.目前,2G连通外平面图的邻点可区别全染色的研究成果比较多,如最大度为3,4,5,6,7的2G连通外平面图的邻点可区别全色数.在这篇文章中,主要运用了分析法和数学归纳法,证明了最大度小于等于3的2G连通外平面图的Smarandachely邻点可区别全色数不超过6.

Smrandachely neighbor point-distinguishing full coloring is the special neighbor point-distinguishing full coloring which is not included in the color set of adjacent two vertices. It further enhances the conditions of neighbor point-distinguishing full coloring. At present, there are many research results on adjacent vertex-distinguishing total coloring of 2-connected outerplanar graphs, for instance the neighbors distinguishable full color number of 2-connected outerplanar graphs with maximum degree of 3, 4, 5, 6 and 7. In this paper, analysis and mathematical in d uction are mainly used to prove that the Smarandachely neighbors distinguishable full color number of 2-connected outerplanar graphs with its maximum degree less than or equal to 3 is not more than 6.