IJPAM: Volume 34, No. 2 (2007)

SOME GRAPHS WITH MAGICAL LABELLING

Ming Yao$^1$, Bing Yao$^2$, Zhongfu Zhang$^3$
$^{1,3}$Department of Mathematics
Lanzhou Vocational Technology College
Lanzhou, 730060, P.R. CHINA
$^{2,3}$College of Mathematics and Information Science
Northwest Normal University
Lanzhou, 730070, P.R. CHINA
$^2$e-mail: [email protected]
$^3$Institute of Applied Mathematics
Lanzhou Jiaotong University
Lanzhou, 730070, P.R. CHINA


Abstract.An edge-magic total labelling of a graph $G$ with $p$ vertices and $q$ edges is a bijective mapping $f$ from $V(G)\cup E(G)$ into $\{1,2, \cdots ,p+q\}$ if there is a positive integer $\lambda _f$ such that $f(u)+f(v)+f(uv)=\lambda _f$ whenever $uv\in E(G)$. We prove $p+q+3\leq \lambda_f \leq 2(p+q)$, and furthermore $\lambda_f\leq 2p+q$ if $1\leq f(u)\leq p$ for any $u\in V(G)$, $G$ is called semt-magical in this case. If $G$ is regular and semt-magical, then $G$ has the uniquely magical constant. We construct several magical graphs of larger orders with other magical graphs of small orders.

Received: September 18, 2006

AMS Subject Classification: 05C78, 05C15

Key Words and Phrases: total labelling, magical labelling, magical trees

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 34
Issue: 2