A stacked (or generalized) prism graph is a simple graph given by the graph
Cartesian product
(Gallian 2007) for positive integers
with
.
It can therefore be viewed formed by connecting
concentric cycle graphs
along spokes.
therefore has
vertices and
edges. Several are illustrated above.
Stacked prims graphs aometimes also called -prism graphs, circular ladder graphs (Gross and Yellen
1999, p. 14) or cylinder graphs (Mertens 2024).
The term "web graph" is sometimes also used to refer to a stacked prism graph (e.g., Horvat and Pisanski 2010), although Koh
(1980) and Gallian (2007) reserve that term for a stacked prism graph with the edges of the outer cycle removed.
Special cases are summarized in the following table.
Since stacked prism graphs are a graph Cartesian product of two unit-distance graphs, the are themselves unit-distance graphs (Horvat and Pisanski 2010).
Precomputed properties of generalized prism graphs are implemented in the Wolfram Language as GraphData["StackedPrism",
m, n
].
Mertens (2024) computed the domination polynomial and numbers of dominating sets for stacked prism
graphs
up to
.