IJPAM: Volume 30, No. 2 (2006)

OF $F_{n}\bigvee P_{n}\bigvee P_{n}$

Xiaoping Wang$^1$, Jingwen Li$^2$, Liang Bian$^3$, Zhongfu Zhang$^4$
Institute of Applied Mathematics
Lanzhou Jiaotong University
Lanzhou 730070, P.R. CHINA
$^4$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 $F_{n}\bigvee P_{n}\bigvee P_{n}$ were obtained.

Received: May 15, 2006

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

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

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 30
Issue: 2