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Stacked Prism Graph


PrismGraphs

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 2007) for positive integers m,n with m>=3. It can therefore be viewed formed by connecting n concentric cycle graphs C_m along spokes. Y_(m,n) therefore has mn vertices and m(2n-1) edges. Several are illustrated above.

Stacked prims graphs aometimes also called (m,n)-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, B. and Pisanski 2010), although Koh (1980) and Gallian (2007) reserve that term for a stacked prism graph Y_(n+1,3) 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 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. DS6. Dec. 21, 2018. https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS6.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.

Cite this as:

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

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