Let $G$ be a connected graph and $g$ be a non-negative integer. The $g$-extra connectivity of $G$ is the minimum cardinality of a set of vertices in $G$, if it exists, whose removal disconnects $G$ and leaves every component with more than $g$ vertices. The strong product $G_1 \boxtimes G_2$ of graphs $G_1=(V_{ 1}, E_{ 1})$ and $G_2=(V_{ 2}, E_{ 2})$ is the graph with vertex set $V(G_1 \boxtimes G_2)=V_{ 1} \times V_{ 2}$, where two distinct vertices $(x_{ 1}, x_{ 2}), (y_{ 1}, y_{ 2}) \in V_{ 1} \times V_{ 2}$ are adjacent in $G_1 \boxtimes G_2$ if and only if $x_{ i}=y_{ i}$ or $x_{ i} y_{ i} \in E_{ i}$ for $i=1, 2$. In this paper, we obtain the $g$-extra connectivity of the strong product of two paths, the strong product of a path and a cycle, and the strong product of two cycles.
Categories: math.CO