Throughout the study on a class of vertex coloring of special graphs, this paper gives the following results: (1) Give vertex coloring number of graph G, 〖JB(|〗S〖JB)|〗=p-3and p∈〖JB({〗4,5,〖JB(〗6〖JB)}〗〖JB)〗 . (2) Prove that graph G of〖JB(|〗S〖JB)|〗>〖SX(〗p〖〗2〖SX)〗 and 〖JB(|〗S〖JB)|〗=p-3has no the p-m class of graph, m≥7and m is positive integer. (3) Prove that χ(G)≤4θ(G)+θ2(G)-1, when〖JB(|〗S〖JB)|〗=p-3. All kinds of vertex coloring number of graph G when〖JB(|〗S〖JB)|〗=p-3are given from these results above, and further it is proven that the conjecture χ(G)≤4θ(G)+θ2(G)-1 is right., which provide some thoughts and methods for further study on this conjecture and the graph vertex coloring.