Summary: Let \(G\) be a graph with vertex set \(V(G)\) and edge set \(E(G)\). For \( u\in V(G) \), \( N_V(u) = \{ w\in V(G) \mid uw \in E(G) \} \) and \( N_E(u) = \{ e\in E(G) \mid e= uv, \text { for some} v \in V(G) \} \). A bijective function \( f: V(G)\cup E(G)\rightarrow \{ 1,2,3,\dots,|V(G) \cup E(G)| \} \) is said to be a vertex-edge neighborhood prime labeling, if for \( u \in V(G)\) with \(\deg(u) = 1\), \(\gcd \{ f(w), f(uw)\mid w\in N_V(u) \} = 1\); for \( u \in V(G)\) with \(\deg(u)>1\), \(\gcd \{ f(w)\mid w\in N_V(u) \} = 1\) and \(\gcd \{ f(e)\mid e\in N_E(u) \} = 1\). A graph which admits a vertex-edge neighborhood prime labeling is called a vertex-edge neighborhood prime graph. In this paper we prove \(K_{m,n} \odot K_1\), \(W_{n} \odot K_1\), \(H_{n} \odot K_1\), \(F_{n} \odot K_1\) and \(S(K_{1,n}) \odot K_1\) are vertex-edge neighborhood prime graphs.