  A rectangle visibility graph (RVG) is represented by assigning to each vertex
a rectangle in the plane with horizontal and vertical sides in such a way that
edges in the graph correspond to unobstructed horizontal and vertical lines of
sight between their corresponding rectangles. To discretize, we consider only
rectangles whose corners have integer coordinates. For any given RVG, we seek a
representation with smallest bounding box as measured by its area, perimeter,
width, or height (height is assumed not to exceed width).
  We derive a number of results regarding these parameters. Using these
results, we show that these four measures are distinct, in the sense that there
exist graphs $G_1$ and $G_2$ with $area(G_1)<area(G_2)$ but
$perimeter(G_2)<perimeter(G_1)$, and analogously for all other pairs of these
parameters. We further show that there exists a graph $G_3$ with
representations $S_1$ and $S_2$ such that $area(G_3)=area(S_1)<area(S_2)$ but
$perimeter(G_3)=perimeter(S_2)<perimeter(S_1)$. In other words, $G_3$ requires
distinct representations to minimize area and perimeter. Similarly, such graphs
exist to demonstrate the independence of all other pairs of these parameters.
  Among graphs with $n \leq 6$ vertices, the empty graph $E_n$ requires largest
area. But for graphs with $n=7$ and $n=8$ vertices, we show that the complete
graphs $K_7$ and $K_8$ require larger area than $E_7$ and $E_8$, respectively.
Using this, we show that for all $n \geq 8$, the empty graph $E_n$ does not
have largest height, width, area, or perimeter among all RVGs on $n$ vertices.
