Probing Graph Proper Total Colorings With Additional Constrained Conditions

Graph colorings are becoming an increasingly useful family of mathematical models for a broad range of applications, such as time tabling and scheduling, frequency assignment, register allocation, computer security and so on. Graph proper total colorings with additional constrained conditions have been investigated intensively in the last decade year. In this article some new graph proper total colorings with additional constrained conditions are defined, and approximations to the chromatic numbers of these colorings are researched, as well as some graphs having these colorings have been verified.

[1]  B. Yao,et al.  On the adjacent-vertex-strongly-distinguishing total coloring of graphs , 2008 .

[2]  Richard H. Schelp,et al.  Adjacent Vertex Distinguishing Edge-Colorings , 2007, SIAM J. Discret. Math..

[3]  Bin Liu,et al.  On the adjacent vertex distinguishing edge colourings of graphs , 2010, Int. J. Comput. Math..

[4]  Chao Yang,et al.  Adjacent vertex distinguishing total colorings of graphs with four distinguishing constraints , 2016, Ars Comb..

[5]  Xiaowei Yu,et al.  Adjacent vertex distinguishing colorings by sum of sparse graphs , 2016, Discret. Math..

[6]  Aijun Dong,et al.  Neighbor sum distinguishing total colorings of graphs with bounded maximum average degree , 2014 .

[7]  B. Yao,et al.  On adjacent-vertex-distinguishing total coloring of graphs , 2005 .

[8]  Richard H. Schelp,et al.  Vertex-distinguishing proper edge-colorings , 1997, Journal of Graph Theory.

[9]  Chao Yang,et al.  A note on graph proper total colorings with many distinguishing constraints , 2016, Inf. Process. Lett..

[10]  Hao Li,et al.  A note on the vertex-distinguishing proper coloring of graphs with large minimum degree , 2001, Discret. Math..

[11]  Wei-Fan Wang,et al.  Adjacent vertex distinguishing edge-colorings of graphs with smaller maximum average degree , 2010, J. Comb. Optim..

[12]  Saieed Akbari,et al.  r-Strong edge colorings of graphs , 2006, Discret. Math..

[13]  P. N. Balister,et al.  Vertex distinguishing colorings of graphs with Delta(G)=2 , 2002, Discret. Math..

[14]  GUANGHUI WANG,et al.  Neighbor Sum Distinguishing Coloring of some Graphs , 2012, Discret. Math. Algorithms Appl..

[15]  Jianfang Wang,et al.  Adjacent strong edge coloring of graphs , 2002, Appl. Math. Lett..

[16]  J. A. Bondy,et al.  Graph Theory , 2008, Graduate Texts in Mathematics.

[17]  András Gyárfás,et al.  Semistrong edge coloring of graphs , 2005 .

[18]  Sandeep Krishna,et al.  Graph Theory and the Evolution of Autocatalytic Networks , 2002, nlin/0210070.

[19]  Hamed Hatami,et al.  Delta+300 is a bound on the adjacent vertex distinguishing edge chromatic number , 2005, J. Comb. Theory, Ser. B.