On super mean labeling of some graphs

Abstract

Let $G$ be a $(p,q)$-graph and : $V(G)\to \{k,k+1,k+2,k+3,\dots ,p+q+k-1\}$ be an injection. For each edge $e=uv$, let $f^{*}(e)=\lceil \frac{f(u)+f(v)}{2}\rceil$. 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 $k$-super mean graph. In this paper, we present $k$-super mean labeling of $C_{2n}(n\ne 2)$ and super mean labeling of Double cycle $C(m,n)$, Dumb bell graph $D(m,n)$ and Quadrilateral snake $Q_n$.