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Stacked Prism Graph


A stacked (or generalized) prism graph Y_(m,n) is a simple graph given by the graph Cartesian product Y_(m,n)=C_m square P_n (Gallian 2025, p. 217) for positive integers m and n with m>=3. Stacked prism graphs are sometimes also called (m,n)-prism graphs or cylinder graphs (Mertens 2024). When n=2, they are prism graphs, also called circular ladder graphs (Gross and Yellen 1999, p. 14). By analogy with the KC graph and KP graph, the stacked prism graph could also be called a "CP graph." The term "web graph" is sometimes also used to refer to a stacked prism graph (e.g., Horvat and Pisanski 2010), while in the convention used here a web graph is obtained from Y_(m,3) by removing the edges of its outer cycle.

PrismGraphs

A stacked prism graph can also be formed by connecting n concentric cycle graphs C_m along spokes that begin at the innermost and end at the outermost cycle. Y_(m,n) therefore has mn vertices and m(2n-1) edges. Several are illustrated above.

Special cases are summarized in the following table.

Since stacked prism graphs are a graph Cartesian product of two unit-distance graphs, they 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 Y_(m,n) up to m,n=24.


See also

Cycle Graph, Graph Cartesian Product, Grid Graph, Prism Graph, Square Graph, Triangle Graph, Web Graph

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References

Gallian, J. "Dynamic Survey of Graph Labeling." Elec. J. Combin., Dynamic Survey DS6, Oct. 30, 2025. https://doi.org/10.37236/27.Horvat, B. and Pisanski, T. "Products of Unit Distance Graphs." Disc. Math. 310, 1783-1792, 2010.Koh, K. M.; Rogers, D. G.; Teo, H. K.; and Yap, K. Y. "Graceful Graphs: Some Further Results and Problems." Congr. Numer. 29, 559-571, 1980.Mertens, S. "Domination Polynomials of the Grid, the Cylinder, the Torus, and the King Graph." 15 Aug 2024. https://arxiv.org/abs/2408.08053.

Referenced on Wolfram|Alpha

Stacked Prism Graph

Cite this as:

Weisstein, Eric W. "Stacked Prism Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StackedPrismGraph.html

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