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To each finite frame $\varphi$ in an inner product space $\mathcal{H}$ weassociate a simple graph $G(\varphi)$, called {\it frame graph}, with thevectors of the frame as vertices and there is an edge between vertices $f$ and$g$ provided that $\langle f, g\rangle \neq 0$ [1]. In this paper the relationbetween the order of $G(\varphi)$ and the dimension of $\mathcal{H}$ isinvestigated for some well-known classes of graphs and their products.

Characterization of some classes of graphs and their products as frame graph