IJPAM: Volume 41, No. 5 (2007)

THE STAR TOTAL COLORING OF $P_{m}\times P_{n}$

Chao Zuo$^1$, Muchun Li$^2$, Ting Zhang$^3$, Changsheng An$^4$
$^{1,2,3,4}$School of Mathematics, Physics and Software Engineering
Lanzhou Jiaotong University
Lanzhou, 730070, P.R. CHINA
$^1$e-mail: andyzuch@163.com


Abstract.The coloring problem of graphs is induced by computer science, which has widely application in networks. The coloring problem of graphs is to configure the colorings of each coloring ways of the graphs. All graphs considered in this paper are finite simple graphs. Let $G=G(V(G), E(G))$ be a graph, where $V(G)$ and $E(G)$ denote the vertex set and edge set of $G$. 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 $\chi_{st}(G)$. It is called the star total chromatic number of $G$. In this paper, we discuss some the star total coloring of graph, and obtain the star total chromatic number of $P_{m}$$\times$$P_{n}$.

Received: May 10, 2007

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

Key Words and Phrases: star total coloring, star total chromatic number, $P_{m}\times P_{n}$

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 41
Issue: 5