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Let $G_1\sq G_2$ denote the graph obtained from $G_1+G_2$ by adding new edgesfrom each vertex of $G_1$ to every vertex of $G_2$. In this paper, the criticalgroups of the graphs $K_m\sq P_n$$(n\geq4)$ and $P_m\sq P_n$$(m\geq4,n\geq5)$are determined.

The critical group of $K_m\vee P_n$ and $P_m\vee P_n$