  A plane graph is said to be a rectangular graph if each of its edges can be
oriented horizontal or vertical, its internal regions are four-sided and it has
a rectangular enclosure. If dual of a planar graph is a rectangular graph, then
the graph is said to be a rectangular dualizable graph (RDG). In this paper, we
present adjacency transformations between RDGs and present polynomial time
algorithms for their transformations. An RDG $\mathcal{G}=(V, E)$ is called
maximal RDG (MRDG) if there does not exist an RDG $\mathcal{G'}=(V, E')$ with
$E' \supset E$. An RDG $\mathcal{G}=(V, E)$ is said to be an edge-reducible if
there exists an RDG $\mathcal{G'}=(V, E')$ such that $E\supset E'$. If an RDG
is not edge-reducible, it is said to be an edge-irreducible RDG. We show that
there always exists an MRDG for a given RDG. We also show that an MRDG is
edge-reducible and can always be transformed to a minimal one (an
edge-irreducible RDG).
