Reachability Results in Plane Trees

Albert Nyariaro; Isaac Owino Okoth

doi:10.33434/cams.936558

Araştırma Makalesi

Reachability Results in Plane Trees

Yıl 2021, , 75 - 88, 30.06.2021

Albert Nyariaro , Isaac Owino Okoth

https://doi.org/10.33434/cams.936558

Öz

In this paper, we obtain closed formulas for the number of reachable vertices in labelled plane trees by paths lengths, sinks, leaf sinks, first children, left most path, non-first children, and non-leaves. Our counting objects are plane trees having their edges oriented from a vertex of lower label towards a vertex of higher label. For each statistic, we obtain the average number of reachable vertices. Moreover, we obtain a counting formula for the number of plane trees on $n$ vertices such that exactly $k\leq n$ are reachable from the root.

Anahtar Kelimeler

Plane tree, Leaf, Sink

Destekleyen Kurum

Maseno University

Kaynakça

[1] R. R. X. Du, J .Yin. Countinglabelledtreeswithagivenindegreesequence. J.Combin.Theory,Ser.A,117(3)(2010),345– 353.
[2] I. O. Okoth. Combinatorics of oriented trees and tree-like structures. PhD Thesis, Stellenbosch University, (2015).
[3] I. O. Okoth, A. O. Nyariaro. Reachability results in labelled t-ary trees. Preprint, (2021).
[4] S. Seo, H. Shin. On the enumeration of rooted trees with ﬁxed size of maximal decreasing trees. Discrete Math.,312(2) (2012), 419–426.
[5] H. S. Wilf. Generatingfunctionology. A. K. Peters, Ltd., Natick, MA, USA, (2006).

Yıl 2021, , 75 - 88, 30.06.2021

Albert Nyariaro , Isaac Owino Okoth

https://doi.org/10.33434/cams.936558

Öz

Kaynakça

[1] R. R. X. Du, J .Yin. Countinglabelledtreeswithagivenindegreesequence. J.Combin.Theory,Ser.A,117(3)(2010),345– 353.
[2] I. O. Okoth. Combinatorics of oriented trees and tree-like structures. PhD Thesis, Stellenbosch University, (2015).
[3] I. O. Okoth, A. O. Nyariaro. Reachability results in labelled t-ary trees. Preprint, (2021).
[4] S. Seo, H. Shin. On the enumeration of rooted trees with ﬁxed size of maximal decreasing trees. Discrete Math.,312(2) (2012), 419–426.
[5] H. S. Wilf. Generatingfunctionology. A. K. Peters, Ltd., Natick, MA, USA, (2006).

Toplam 5 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Matematik
Bölüm	Makaleler
Yazarlar	Albert Nyariaro 0000-0002-2997-0241 Isaac Owino Okoth 0000-0003-4503-4733
Yayımlanma Tarihi	30 Haziran 2021
Gönderilme Tarihi	12 Mayıs 2021
Kabul Tarihi	25 Haziran 2021
Yayımlandığı Sayı	Yıl 2021

Kaynak Göster

APA	Nyariaro, A., & Okoth, I. O. (2021). Reachability Results in Plane Trees. Communications in Advanced Mathematical Sciences, 4(2), 75-88. https://doi.org/10.33434/cams.936558
AMA	Nyariaro A, Okoth IO. Reachability Results in Plane Trees. Communications in Advanced Mathematical Sciences. Haziran 2021;4(2):75-88. doi:10.33434/cams.936558
Chicago	Nyariaro, Albert, ve Isaac Owino Okoth. “Reachability Results in Plane Trees”. Communications in Advanced Mathematical Sciences 4, sy. 2 (Haziran 2021): 75-88. https://doi.org/10.33434/cams.936558.
EndNote	Nyariaro A, Okoth IO (01 Haziran 2021) Reachability Results in Plane Trees. Communications in Advanced Mathematical Sciences 4 2 75–88.
IEEE	A. Nyariaro ve I. O. Okoth, “Reachability Results in Plane Trees”, Communications in Advanced Mathematical Sciences, c. 4, sy. 2, ss. 75–88, 2021, doi: 10.33434/cams.936558.
ISNAD	Nyariaro, Albert - Okoth, Isaac Owino. “Reachability Results in Plane Trees”. Communications in Advanced Mathematical Sciences 4/2 (Haziran 2021), 75-88. https://doi.org/10.33434/cams.936558.
JAMA	Nyariaro A, Okoth IO. Reachability Results in Plane Trees. Communications in Advanced Mathematical Sciences. 2021;4:75–88.
MLA	Nyariaro, Albert ve Isaac Owino Okoth. “Reachability Results in Plane Trees”. Communications in Advanced Mathematical Sciences, c. 4, sy. 2, 2021, ss. 75-88, doi:10.33434/cams.936558.
Vancouver	Nyariaro A, Okoth IO. Reachability Results in Plane Trees. Communications in Advanced Mathematical Sciences. 2021;4(2):75-88.