  We propose new families of graphs which exhibit quantum perfect state
transfer. Our constructions are based on the join operator on graphs, its
circulant generalizations, and the Cartesian product of graphs. We build upon
the results of Ba\v{s}i\'{c} et al \cite{bps09,bp09} and construct new integral
circulants and regular graphs with perfect state transfer. More specifically,
we show that the integral circulant $\textsc{ICG}_{n}(\{2,n/2^{b}\} \cup Q)$
has perfect state transfer, where $b \in \{1,2\}$, $n$ is a multiple of 16 and
$Q$ is a subset of the odd divisors of $n$. Using the standard join of graphs,
we also show a family of double-cone graphs which are non-periodic but exhibit
perfect state transfer. This class of graphs is constructed by simply taking
the join of the empty two-vertex graph with a specific class of regular graphs.
This answers a question posed by Godsil \cite{godsil08}.
