IJPAM: Volume 37, No. 4 (2007)

ON THE VERTEX-DISTINGUISHING
TOTAL COLORING OF $P_m\vee F_n$

Zhao Chuancheng$^1$, Liu Jun$^2$, Ren Zhiguo$^3$,
Bao Shitang$^4$, Zhang Zhongfu$^5$
$^{1,2,3,4,5}$Institute of Information and Application
Lanzhou City College
Lanzhou, 730070, P.R. CHINA
$^1$e-mail: [email protected]


Abstract.Let $G(V,E)$ be a simple graph, $f$ be a mapping from $V(G)\cup E(G)$ to $\{1,2,\cdots,k\}$. Let $C_f(v)=\{f(v)\}\cup \{f(vw)\vert w\in V(G),vw\in E(G)\}$ for every $v\in E(G)$. If $f$ is a k-proper-total-coloring, and for $\forall u,v\in V(G)$, we have $C_f(u)\neq C_f(v)$, then $f$ is called the k-vertex-distinguishing total coloring ($k$-VDEC for short). Let $\chi^{'}_{vt}(G)=\min\{k\vert$G has a k-vertex-distinguishing total coloring$\}$. Then $\chi^{'}_{vt}(G)$ is called the vertex-distinguishing total chromatic number. The total chromatic numbers on $P_m\vee F_n$ are presented in this paper.

Received: March 19, 2007

AMS Subject Classification: 68R10

Key Words and Phrases: graph, path, fan, vertex-distinguishing total coloring, total chromatic number

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 37
Issue: 4