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
2172
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[![<span style=]()
{" src="https://mathworld.wolfram.com/images/equations/BananaTree/Inline5.svg" style="height:22px; width:6px" />"BananaTree", ![<span style=]()
{" src="https://mathworld.wolfram.com/images/equations/BananaTree/Inline6.svg" style="height:22px; width:6px" />n, k![<span style=]()
}" src="https://mathworld.wolfram.com/images/equations/BananaTree/Inline7.svg" style="height:22px; width:6px" />![<span style=]()
}" src="https://mathworld.wolfram.com/images/equations/BananaTree/Inline8.svg" style="height:22px; width:6px" />].
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.
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