LAUSR

Let $G=\left(V\left(G\right),E\left(G\right)\right)$ be a connected graph. A subset $F\subseteq V\left(G\right)$ is called a $g$ -good-neighbor cut if $G-F$ is disconnected and each vertex of $G-F$ has at least $g$ neighbors. The $g$ -good-neighbor connectivity of $G$ is the minimum cardinality of $g$ -good-neighbor cuts. The $n$ -dimensional modified bubble-sort graph ${\text{MB}}_n$ is a special Cayley graph. It has many good properties. In this paper, we prove that the 3-good-neighbor connectivity of ${\text{MB}}_n$ is $8n-24$ for $n\ge 6$ .