Let G be a finite group and Γ\documentclass[12pt]{minimal}
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\begin{document}$$\Gamma $$\end{document} a G-symmetric graph. Suppose that G is imprimitive on V(Γ)\documentclass[12pt]{minimal}
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\begin{document}$$V(\Gamma )$$\end{document} with B a block of imprimitivity and B:={Bg:g∈G}\documentclass[12pt]{minimal}
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\begin{document}$$ \mathcal {B} := \{B^g: g\in G\}$$\end{document} is a system of imprimitivity of G on V(Γ)\documentclass[12pt]{minimal}
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\begin{document}$$V(\Gamma )$$\end{document}. Define ΓB\documentclass[12pt]{minimal}
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\begin{document}$$\Gamma _{\mathcal {B}}$$\end{document} to be the graph with vertex set B\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {B}$$\end{document}, such that two blocks B,C∈B\documentclass[12pt]{minimal}
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\begin{document}$$B, C \in \mathcal {B}$$\end{document} are adjacent if and only if there exists at least one edge of Γ\documentclass[12pt]{minimal}
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\begin{document}$$\Gamma $$\end{document} joining a vertex in B and a vertex in C. Set v=|B|\documentclass[12pt]{minimal}
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\begin{document}$$v=|B|$$\end{document} and k:=|Γ(C)∩B|\documentclass[12pt]{minimal}
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\begin{document}$$k := |\Gamma (C)\cap B|$$\end{document} where C is adjacent to B in ΓB\documentclass[12pt]{minimal}
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\begin{document}$$\Gamma _{\mathcal {B}}$$\end{document} and Γ(C)\documentclass[12pt]{minimal}
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\begin{document}$$\Gamma (C)$$\end{document} denotes the set of vertices of Γ\documentclass[12pt]{minimal}
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\begin{document}$$\Gamma $$\end{document} adjacent to at least one vertex in C. Assume that k=v-p≥1\documentclass[12pt]{minimal}
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\begin{document}$$k=v-p\ge 1$$\end{document}, where p is an odd prime, and ΓB\documentclass[12pt]{minimal}
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\begin{document}$$\Gamma _{\mathcal {B}}$$\end{document} is (G, 2)-arc-transitive. In this paper , we show that if the group induced on each block is an affine group then v=6\documentclass[12pt]{minimal}
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\begin{document}$$v=6$$\end{document}.
