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Banana Tree

BananaTree

An (n,k)-banana tree, as defined by Chen et al. (1997), is a graph obtained by connecting one leaf of each of n copies of an k-star graph with a single root vertex that is distinct from all the stars.

Banana trees are graceful (Sethuraman and J. Jesintha 2009, Gallian 2018).

The (n,k)-banana tree has rank polynomial

R(x)=(1+x)^(nk).

Precomputed properties of a number of banana trees is implemented in the Wolfram Language as GraphData[{"BananaTree", {n, k}}].

See also

Caterpillar Graph, Lobster Graph, Star Graph, Tree

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References

Chen, W.-C.; Lu, H.-I; and Yeh, Y.-N. "Operations of Interlaced Trees and Graceful Trees." Southeast Asian Bull. Math. 21, 337-348, 1997.Gallian, J. "Dynamic Survey of Graph Labeling." Elec. J. Combin. DS6. Oct. 30, 2025. https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS6.Horton, M. "Graceful Trees: Statistics and Algorithms." Bachelor of Computing with Honours thesis. University of Tasmania, 2003. https://eprints.utas.edu.au/19/1/GracefulTreesStatisticsAndAlgorithms.pdf.Sethuraman, G.; and Jesintha, J. "All Banana Trees Are Graceful." Advances Appl. Disc. Math. 4, 53-64, 2009.

Referenced on Wolfram|Alpha

Banana Tree

Cite this as:

Weisstein, Eric W. "Banana Tree." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BananaTree.html

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