IJPAM: Volume 34, No. 4 (2007)

ON THE ADJACENT STRONG EDGE COLORING
OF $W_{n}\vee C_{n}\vee C_{n}$

Liang Bian$^1$, Zhongfu Zhang$^2$
$^{1, 2}$Institute of Applied Mathematics
Lanzhou Jiaotong University
Lanzhou, 730070, P.R. CHINA
$^2$e-mail: zhang_zhong_fu@yahoo.com.cn


Abstract.A $k$-proper edge coloring of a graph $G$ is called $k$-adjacent strong edge coloring, if it is satisfied with $C(u)\neq C(v)$ for $uv\in E(G)$, where $C(u)=\{f(uv)\vert uv\in E(G)\}$, then $f$ is called $k$-adjacent strong edge coloring of $G$, which is abbreviated $k$-ASEC of $G$, and the adjacent strong edge chromatic number of $G$, denoted by $\chi\, '_{as}(G)$, is the minimal number of colors in an adjacent strong edge coloring of $G$. In this paper, the adjacent strong edge coloring of $W_{n}\vee C_{n}\vee C_{n}$ is obtained.

Received: October 16, 2006

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

Key Words and Phrases: adjacent strong edge coloring, join-graph, wheel, cycle

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 34
Issue: 4