  It is well known that if a network topology is a path or line and the states
of vertices or nodes evolve according to the consensus policy, then the network
is Laplacian controllable by an input connected to its terminal vertex. In this
work a path is regarded as the resulting graph after interconnecting a finite
number of two-vertex antiregular graphs and then possibly connecting one more
vertex. It is shown that the single-input Laplacian controllability of a path
can be extended to the case of interconnecting a finite number of $k$-vertex
antiregular graphs with or without one more vertex appended, for any positive
integer $k$. The methods to interconnect these antiregular graphs and to select
the vertex for connecting the single input that renders the network Laplacian
controllable are presented as well.
