IJPAM: Volume 35, No. 2 (2007)

ON THE ADJACENT VERTEX-DISTINGUISHING
TOTAL COLORING OF $C_{n,n}$

Bing Wei$^1$, Ming Yao$^2$, Donghan Zhang$^3$, Zhongfu Zhang$^4$
$^1$Department of Mathematics
Huizhou College
Guangdong, 516007, P.R. CHINA
e-mail: wb@hzu.edu.cn
$^2$Department of Mathematics
Lanzhou Petrochemical College of Vocational Technology
Lanzhou, 730060, P.R. CHINA
$^3$Institute of Applied Mathematics
Lanzhou Jiaotong University
Lanzhou, 730070, P.R. CHINA


Abstract.Let f be the proper total coloring of G, if any adjacent vertex u and v, $f(u)\cup \{f(uw)\vert uw\in E(G)\}\neq
f(v)\cup \{f(vw)\vert vw\in E(G)\}$, then, f is called the adjacent vertex-distinguishing total coloring, the minmum k is called the adjacent vertex-distinguishing total chromatic number. In this paper, we study the adjacent vertex-distinguishing total chromatic number of $C_{n,n}$.

Received: December 11, 2006

AMS Subject Classification: 05C15, 68R10

Key Words and Phrases: graph, adjacent vertex-distinguishing total coloring of graphs

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 35
Issue: 2