Constructing connected bicritical graphs with edge-connectivity 2

A graph $G$ is said to be bicritical if the removal of any pair of vertices decreases the domination number of $G$. For a bicritical graph $G$ with the domination number $t$, we say that $G$ is $t$-bicritical. Let $\lambda \left(G\right)$ denote the edge-connectivity of $G$. In [2], Brigham et al. (2005) posed the following question: If $G$ is a connected bicritical graph, is it true that $\lambda \left(G\right)\ge 3?$In this paper, we give a negative answer toward this question; namely, we give a construction of infinitely many connected $t$-bicritical graphs with edge-connectivity $2$ for every integer $t\ge 5$. Furthermore, we give some sufficient conditions for a connected $5$-bicritical graph to have $\lambda \left(G\right)\ge 3$.