IJPAM: Volume 25, No. 2 (2005)

ABOUT THE COLORING PROPERTIES OF
$F_M$ GENERAL MYCIELSKI-GRAPH

Huiying Qiang$^1$, Zhongfu Zhang$^2$, Fugang Chao$^3$
$^{1,2,3}$Institute of Applied Mathematics
Lanzhou Jiaotong University
Lanzhou, 730070, P.R. CHINA
$^1$e-mail: qhy2005ww@126.com


Abstract.It is $M_n(G)$ called general Mycielski graph $G$, $n$ is natural number, if

\begin{displaymath} V(M_n(G)) =\{v_{00},v_{01},...v_{0m};v_{10},v_{11},...v_{1m};...;v_{n0},v_{n1},...v_{nm}\};\end{displaymath}


\begin{multline*} E(M_n(G))=E(G)\cup{\{v_{ij}v_{(i+1)k}\vert v_{0j}v_{0k}\in{E(G)},} \\ 1\leq{j},k\leq{m},i=0,1,\cdots,n-1\}, \end{multline*}

The general Mycielski graph of fan with order $m+1$ is noted $M_n(F_{m})$. In this paper, some results of $M_n(F_{m})$ graphs were obtained.

Received: October 21, 2005

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

Key Words and Phrases: general Mycielski graph, total coloring, adjacent-vertex-distinguishing total coloring

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 25
Issue: 2