1. Vince is a natural generalization of chromatic number.

2. The adjacent vertex distinguishing total chromatic number is obtained for the flower graph.

3. The edge chromatic number of join graph with fan and complete balanced bipartite graph was obtained.

4. This paper discusses the upper chromatic number of the Cartesian product of co - hypergraphs.

5. In this paper a estimate of the harmonious chromatic number a complete 5-ary tree was given.

6. The adjacent vertex distinguishing total chromatic number is obtained for the middle graphs of path, cycle, star and fan graph.

7. The adjacent vertex - distinguishing total chromatic number of Subdivision of Fn , Wn, Km, n was got paper.

7. try its best to collect and build good sentences.

8. A new algorithm of chromatic number and minimal coloring of a given graph is given.

9. It is not easy to see that there are triangle - free graphs of large chromatic number.

10. In the sixth part, the probability estimates of vertex-adjacent vertex distinguishing total chromatic number of some graphs are discussed.

11. The company now has five multi-color intaglio printing machine and a hot transfer printed cloth production lines, printing chromatic number to seven-color maximum.

12. And check that the separation proof separations are correct and the chromatic number of separation.

13. In this paper, Euler's formula and Handshaking lemma is used to obtain the face chromatic number of a planar graph by solving equations.

14. With this characterization, the bandwidth, topological bandwidth and the path chromatic number for unit interval graphs are determined.

15. The minimum number of colors required for an adjacent vertex-distinguishing total coloring of a simple graph G is called the adjacent vertex-distinguishing total chromatic number, denoted by xat(G).