IJPAM: Volume 31, No. 1 (2006)

OF $P_{m}\vee P_{n}$

Yaodong Cheng$^1$, Donghan Zhang$^2$
$^1$School of Mathematics and Software Engineering
Lanzhou Jiaotong University
Lanzhou, 730000, P.R. CHINA
$^1$e-mail: chengydong@mail.lzjtu.cn

Abstract.Let $G(V,E)$ be a connected graph. A $k$-proper edge coloring $f$ of $G(V,E)$ is said to be a $k$-vertex-distinguishing edge coloring iff $C(u)\not= C(v)$ for $\forall u,v \in V(G)$, $u\ne v$, where $C(u) =\set{f(uv)\vert uv\in E(G)}$; and $\chi_{vd}'(G)=\min\set{k\vert\text{there exists a $k$-VDEC of $G$}}$ is called the vertex-distinguishing edge chromatic number. In this paper, we obtain the vertex-distinguishing edge chromatic number of the join graphs $P_{m}\vee P_{n}$.

Received: July 10, 2006

AMS Subject Classification: 05C15, 68R10

Key Words and Phrases: path, complete graph, join-graph, vertex-distinguishing edge chromatic number

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 31
Issue: 1