IJPAM: Volume 56, No. 1 (2009)

SOME CONSTRUCTIONS OF $k$-SUPER MEAN GRAPHS

P. Jeyanthi$^1$, D. Ramya$^2$, P. Thangavelu$^3$
$^1$Department of Mathematics
Govindammal Aditanar College for Women
Tiruchendur, Tamil Nadu, 628 215, INDIA
e-mail: [email protected]
$^2$Department of Mathematics
Dr. Sivanthi Aditanar College of Engineering
Tiruchendur, Tamil Nadu, 628 215, INDIA
e-mail: [email protected]
$^3$Department of Mathematics
Aditanar College of Arts and Science
Tiruchendur, Tamil Nadu, 628 215, INDIA


Abstract.Let $G$ be a $(p, q)$ graph and $f : V (G)\rightarrow \{1,2,3,\dots,p + q\}$ be an injection. For each edge $e = uv,$ let $f^*(e) = (f(u) + f(v))/2$ if $f(u)+f(v)$ is even and $f^*(e)=(f(u) + f(v) + 1)/2$ if $f(u)+f(v)$ is odd. Then $f$ is called a super mean labeling if $f(V)\cup \{f^*(e) : e\in E(G)\} = \{1,2,3,\dots, p+q\}.$ A graph that admits a super mean labeling is called a super mean graph. Let $G$ be a $(p, q)$ graph and $f: V(G)\rightarrow \{1,2,3,\dots, p+q +k-1\}$ be an injection. For each edge $e = uv,$ let $f^*(e)=\left\lceil\frac{f(u)+f(v)}{2}\right\rceil$. Then $f$ is called a $k$-super mean labeling if $f(V)\cup \{f^*(e): e\in E(G)\}= \{k, k+1, k+2,\dots, p+q+k-1\}.$ A graph that admits a $k$-super mean labeling is called a $k$-super mean graph. In this paper we present super mean labeling of $C_m\cup C_n$ and $T_p$-tree and also we construct some $k$-super mean graphs.

Received: August 9, 2009

AMS Subject Classification: 05C78

Key Words and Phrases: super mean labeling, super mean graph, $k$-super mean labeling, $k$-super mean graph

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 56
Issue: 1