IJPAM: Volume 41, No. 6 (2007)

ON THE STAR TOTAL CHROMATIC NUMBER OF
MYCIELSKI GRAPHS OF PATH AND CYCLE

Jinwen Li$^1$, Muchun Li$^2$, Baogeng Xu$^3$,
Ting Zhang$^4$, Ergeng Liu$^5$, Jieru Du$^6$
$^1$School of Information and Electrical Engineering
Lanzhou Jiaotong University
Lanzhou, 730070, P.R. CHINA
$^1$e-mail: zhangting1389@126.com
$^{2,4,6}$ School of Mathematics, Physics and Software Engineering
Lanzhou Jiaotong University
Lanzhou, 730070, P.R. CHINA
$^{3,5}$Department of Mathematics
East China Jiaotong University
Jiaotong, P.R. CHINA


Abstract.A proper total $k$-coloring of a graph $G$ is a star total $k$-coloring if the colorings of vertices and edges of any path of length 3 in $G$ are all different. The least number of $k$ spanning over all star total $k$-colorings of $G$, denoted by $\chi_{st}(G)$, is called the star total chromatic number of $G$. In this paper, we obtained the star total chromatic numbers of Mycielski of path and cycle graphs.

Received: July 5, 2007

AMS Subject Classification: 05C15, 68R10, 94C15

Key Words and Phrases: path, cycle, Mycielski graph, star total chromatic number

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 41
Issue: 6