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Banana Tree

المؤلف:  Chen, W.-C.; Lu, H.-I; and Yeh, Y.-N.

المصدر:  "Operations of Interlaced Trees and Graceful Trees." Southeast Asian Bull. Math. 21

الجزء والصفحة:  ...

20-3-2022

2551

Banana Tree

An -banana tree, as defined by Chen et al. (1997), is a graph obtained by connecting one leaf of each of  copies of an -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 -banana tree has rank polynomial

Precomputed properties of a number of banana trees is implemented in the Wolfram Language as GraphData[{" src="https://mathworld.wolfram.com/images/equations/BananaTree/Inline5.svg" style="height:22px; width:6px" />"BananaTree", {" src="https://mathworld.wolfram.com/images/equations/BananaTree/Inline6.svg" style="height:22px; width:6px" />n, k}" src="https://mathworld.wolfram.com/images/equations/BananaTree/Inline7.svg" style="height:22px; width:6px" />}" src="https://mathworld.wolfram.com/images/equations/BananaTree/Inline8.svg" style="height:22px; width:6px" />].

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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. Dec. 21, 2018.

 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.