### Odd mean labeling on some new families of graphs

#### Abstract

A graph $G=(V(G),E(G))$ with $p$ vertices and $q$ edges is said to be an \textit{odd mean graph} if there is an injection $\textit{f}:V(G)\rightarrow\{0,1,2,\ldots,2q-1\}$ and the induced function $\textit{f*}:E(G)\rightarrow\{1,3,5,\ldots,2q-1\}$ defined as $f*(uv)=\begin{cases} \frac{f(u)+f(v)}{2}; \, \text{ if } f(u)+f(v) \text{ is even}\\ \frac{f(u)+f(v)+1}{2}; \, \text{ if } f(u)+f(v) \text{ is odd} \end{cases}$ is a bijection. In this paper we investigate some new families of odd mean graphs.

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