|Table of Contents|

[1] Feng Yun, Lin Wensong,. Adjacent vertex-distinguishing total colorings of K^-ss∨Ktt [J]. Journal of Southeast University (English Edition), 2013, 29 (2): 226-228. [doi:10.3969/j.issn.1003-7985.2013.02.021]

Adjacent vertex-distinguishing total colorings of K^-ss∨Ktt()

Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

2013 2
Research Field:
Mathematics, Physics, Mechanics
Publishing date:


Adjacent vertex-distinguishing total colorings of K^-ss∨Ktt
Feng Yun Lin Wensong
Department of Mathematics, Southeast University, Nanjing 211189, China
adjacent vertex-distinguishing total coloring adjacent vertex-distinguishing total chromatic number join graph
Let G be a simple graph and f be a proper total k-coloring of G. The color set of each vertex v of G is the set of colors appearing on v and the edges incident to v. The coloring f is said to be an adjacent vertex-distinguishing total coloring if the color sets of any two adjacent vertices are distinct. The minimum k for which such a coloring of G exists is called the adjacent vertex-distinguishing total chromatic number of G. The join graph of two vertex-disjoint graphs is the graph union of these two graphs together with all the edges that connect the vertices of one graph with the vertices of the other. The adjacent vertex-distinguishing total chromatic numbers of the join graphs of an empty graph of order s and a complete graph of order t are determined.


[1] Zhang Z, Qiu P, Xu B, et al. Vertex-distinguishing total coloring of graphs [J]. Ars Combin, 2008, 87(2): 33-45.
[2] Burris A C, Schelp R H. Vertex-distinguishing proper edge-colourings [J]. J Graph Theory, 1997, 26(2):73-82.
[3] Bazgan C, Harkat-Benhamdine A, Li H, et al. On the vertex-distinguishing proper edge-coloring of graphs [J]. J Combin Theory Ser B, 1999, 75(2): 288-301.
[4] Balister P N, Bollobàs B, Schelp R H. Vertex distinguishing colorings of graphs with Δ(G)=2 [J]. Discrete Math, 2002, 252(2): 17-29.
[5] Zhang Z, Liu L, Wang J. Adjacent strong edge coloring of graphs [J]. Appl Math Lett, 2002, 15(5): 623-626.
[6] Zhang Z, Chen X, Li J, et al. On adjacent-vertex-distinguishing total coloring of graphs [J]. Sci China Ser A, 2005, 48(3): 289-299.
[7] Chen X. Adjacent-vertex-distinguishing total chromatic numbers on K2n+1-E(P3)[J]. Int J Pure Appl Math, 2004, 13(1): 19-27.
[8] Bondy J A, Murty U S R. Graph theory [M]. New York: Springer, 2008.
[9] Hulgan J. Concise proofs for adjacent vertex-distinguishing total colorings [J]. Discrete Math, 2009, 309(8): 2548-2550.
[10] West D B. Introduction to graph theory [M]. 2nd ed. London: Prentice Hall, 2001.


Biographies: Feng Yun(1981—), male, graduate; Lin Wensong(corresponding author), male, doctor, professor, wslin@seu.edu.cn.
Foundation item: The Fundamental Research Funds for the Central Universities of China(No.3207013904).
Citation: Feng Yun, Lin Wensong.Adjacent vertex-distinguishing total colorings of K^-ss∨Ktt[J].Journal of Southeast University(English Edition), 2013, 29(2):226-228.[doi:10.3969/j.issn.1003-7985.2013.02.021]
Last Update: 2013-06-20