Trees with large numbers of subtrees

Xiao, Yuzhi; Zhao, Haixing; Liu, Zhen; Mao, Yaping

doi:10.1080/00207160.2015.1109640

Cited by 21 publications

(10 citation statements)

References 18 publications

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“…K j 1,22 (12 ≤ j ≤ 22) grows linearly with the increase of j. Moreover, from Table 3 and Figure 7, we see that W n (3 ≤ n ≤ 24) increases first in the interval [3,8] and reaches the maximum value when n = 8, and then decreases gradually in the interval [9,24] and approximates the limit value of 0.8135.…”

Section: Subtree Densities Of K J 1n and W Nmentioning

confidence: 69%

“…Finding and/or enumerating special topological structures or graph patterns has become an important problem due to their applications including, to name a few, frequent subgraphs mining [5], network optimization design [6,7], and local network reliability [8,9]. In particular, the subtree number has also been shown to be correlated to phylogenetic reconstruction [10] and various chemical indices such as the Wiener index (closely correlated with the boiling point of paraffin [3]), the Merrifield-Simmons index, and the Hosoya index [11].…”

Section: Introductionmentioning

confidence: 99%

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On Subtrees of Fan Graphs, Wheel Graphs, and “Partitions” of Wheel Graphs under Dynamic Evolution

Wang

et al. 2019

Mathematics

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The number of subtrees, or simply the subtree number, is one of the most studied counting-based graph invariants that has applications in many interdisciplinary fields such as phylogenetic reconstruction. Motivated from the study of graph surgeries on evolutionary dynamics, we consider the subtree problems of fan graphs, wheel graphs, and the class of graphs obtained from “partitioning” wheel graphs under dynamic evolution. The enumeration of these subtree numbers is done through the so-called subtree generation functions of graphs. With the enumerative result, we briefly explore the extremal problems in the corresponding class of graphs. Some interesting observations on the behavior of the subtree number are also presented.

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Section: Subtree Densities Of K J 1n and W Nmentioning

confidence: 69%

Section: Introductionmentioning

confidence: 99%

On Subtrees of Fan Graphs, Wheel Graphs, and “Partitions” of Wheel Graphs under Dynamic Evolution

Wang

et al. 2019

Mathematics

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“…As a representative structural based index, the subtree number index STN(G) of a graph G (also known as ρ-index [7,8]), which is defined as the number of nonempty labeled subtrees of G, plays an important role in areas such as biological reconstruction [9], reliable network construction [10], and machine learning [11] and therefore has attracted much attention in recent years.…”

Section: Introductionmentioning

confidence: 99%

On Subtree Number Index of Generalized Book Graphs, Fan Graphs, and Wheel Graphs

Sun

Zhao

et al. 2021

Journal of Mathematics

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With generating function and structural analysis, this paper presents the subtree generating functions and the subtree number index of generalized book graphs, generalized fan graphs, and generalized wheel graphs, respectively. As an application, this paper also briefly studies the subtree number index and the asymptotic properties of the subtree densities in regular book graphs, regular fan graphs, and regular wheel graphs. The results provide the basis for studying novel structural properties of the graphs generated by generalized book graphs, fan graphs, and wheel graphs from the perspective of the subtree number index.

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“…, e m }, the subtree number index, denoted by ST (G), is defined as the total number of non-empty subtrees of G. Related to subtrees, a BC-subtree is a subtree in which the distances between any two leaves are even. Similar to the subtree number index, we define the BC-subtree number index, denoted by BST (G), as the total number of non-empty BC-subtrees of G. Both of these indices appeared to have applications in the design of reliable communication network [1], bioinformatics [2], and characterizing structural properties of molecular and graphs [3,4,5,6,7,8,9]. By way of generating functions, Yan and Yeh presented the algorithms of enumerating subtrees of trees [10].…”

Section: Introductionmentioning

confidence: 99%

Subtrees and BC-subtrees of maximum degree no more than k in trees

Yu¹,

Li²,

Jin³

et al. 2021

Preprint

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The subtrees and BC-subtrees (subtrees where any two leaves are at even distance apart) have been extensively studied in recent years. Such structures, under special constraints on degrees, have applications in many fields. Through an approach based on generating functions, we present recursive algorithms for enumerating various subtrees and BC-subtrees of maximum degree ≤ k in trees. The algorithms are illustrated through detailed examples. We also briefly discuss, in trees, the densities of subtrees (resp. BC-subtrees) of maximum degree ≤ k(≥ 2) among all subtrees (resp. BC-subtrees).

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Trees with large numbers of subtrees

Cited by 21 publications

References 18 publications

On Subtrees of Fan Graphs, Wheel Graphs, and “Partitions” of Wheel Graphs under Dynamic Evolution

On Subtrees of Fan Graphs, Wheel Graphs, and “Partitions” of Wheel Graphs under Dynamic Evolution

On Subtree Number Index of Generalized Book Graphs, Fan Graphs, and Wheel Graphs

Subtrees and BC-subtrees of maximum degree no more than k in trees

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