Subtrees of spiro and polyphenyl hexagonal chains

Yu, Yang; Liu, Hongbo; Wang, Hua; Fu, Hongsun

doi:10.1016/j.amc.2015.06.094

Cited by 32 publications

(24 citation statements)

References 42 publications

(61 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Specially, by taking (p 1 , p 2 ) = (1, 0), (0, 1) or (0, 0), respectively, and Theorem 3.1, we have the following. The results of Corollary 3.2 agree with the subtree numbers of O n , M n and P n presented in [26].…”

Section: Random Polyphenylene Chainsupporting

confidence: 86%

“…The subtree number index STN(G) of a graph G is a structure-based index, defined as the total number of non-empty subtrees of G. It is discovered to have applications in the design of reliable communication network [21], bioinformatics [11], and characterizing physicochemical and structural properties of molecular graphs [13,26,25]. In recent years there have been related works on enumerating subtrees [22,15,3,2,28], characterizing extremal graphs and values [16,29,10,30], analyzing relations with other topological indices such as the Wiener index [26,25,17,19], average order and density of subtrees [18,9,6].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The expected subtree number index in random polyphenylene and spiro chains

Sun

Jun

et al. 2020

Discrete Applied Mathematics

Self Cite

View full text Add to dashboard Cite

The subtree number index STN(G) of a simple graph G is the number of nonempty subtrees of G. It is a structural and counting topological index that has received more and more attention in recent years. In this paper we first obtain exact formulas for the expected values of subtree number index of random polyphenylene and spiro chains, which are molecular graphs of a class of unbranched multispiro molecules and polycyclic aromatic hydrocarbons. Moreover, we establish a relation between the expected values of the subtree number indices of a random polyphenylene and its corresponding hexagonal squeeze. We also present the average values for subtree number indices with respect to the set of all polyphenylene and spiro chains with n hexagons.

show abstract

Section: Random Polyphenylene Chainsupporting

confidence: 86%

Section: Introductionmentioning

confidence: 99%

The expected subtree number index in random polyphenylene and spiro chains

Sun

Jun

et al. 2020

Discrete Applied Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…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]. Research results also show that there exists an amazing "negative correlation" between the number of subtrees and the Wiener index [12][13][14][15][16][17]. Therefore, the subtree number index can indirectly characterize the physical-chemical characteristics of molecules.…”

Section: Introductionmentioning

confidence: 96%

“…By using "generating functions", Yan and Yeh [4] presented a linear-time algorithm to evaluate the subtree weight sum of a tree, leading to an algorithmic approach to compute the subtree number of a tree. Following this approach and more recently, Yang et al [32,33] proposed enumerating algorithms for BC-subtrees of trees, unicyclic, and edge-disjoint bicyclic graphs and computed the subtree number on spiro and polyphenyl hexagonal chains [17]. With structure mapping and weights transferring of cycles, Yang et al [34] also presented enumerating algorithms for subtrees of hexagonal and phenylene chains.…”

Section: Introductionmentioning

confidence: 99%

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

Wang

et al. 2019

Mathematics

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…Xiao et al [8] showed that 5 + n + 2 n−3 ≤ η(T) ≤ 2 n−1 + n − 1 for any tree T with n vertices. Yang et al [9,10] studied the number of subtrees in spiro and polyphenyl hexagonal chains and hexagonal and phenylene chains, respectively. For more results on this topic, we refer the readers to references [11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Entropy and Enumeration of Subtrees in a Cactus Network

2020

View full text Add to dashboard Cite

For a given network, the number of spanning trees is a key parameter to measure its reliability in edge failure cases, while the number of subtrees is a key parameter to measure its reliability in both vertex and edge failures cases. Zhang et al. investigated the entropy of spanning trees, spanning forests and connected spanning subgraphs of Koch networks. In this paper, we extend Koch networks to 3-cactus networks, and study the entropy of subtrees of 3-cactus networks. We present a linear algorithm to count the number of subtrees in a 3-cactus network, determine the upper and lower bounds of the entropy of subtrees of these networks and characterize those attaining the extremal values. As an application, a linear algorithm is developed to count the number of subtrees in Koch networks, with complexity O(g), where g is the number of iterations. Finally, we determine the entropy of subtrees of Koch networks.

show abstract

Subtrees of spiro and polyphenyl hexagonal chains

Cited by 32 publications

References 42 publications

The expected subtree number index in random polyphenylene and spiro chains

The expected subtree number index in random polyphenylene and spiro chains

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

Entropy and Enumeration of Subtrees in a Cactus Network

Contact Info

Product

Resources

About