Algorithms Based on Path Contraction Carrying Weights for Enumerating Subtrees of Tricyclic Graphs

2020 ◽  
Author(s):  
Yu Yang ◽  
Beifang Chen ◽  
Guoping Zhang ◽  
Yongming Li ◽  
Daoqiang Sun ◽  
...  
Keyword(s):  
Structural Property ◽  
Generating Function ◽  
Difficult Problem ◽  
The Novel ◽  
Structural Decomposition ◽  
General Graph ◽  
Tricyclic Graphs ◽  
Cycle Structures ◽  
Bicyclic Graphs

Abstract The subtree number index of a graph, defined as the number of subtrees, attracts much attention recently. Finding a proper algorithm to compute this index is an important but difficult problem for a general graph. Even for unicyclic and bicyclic graphs, it is not completely trivial, though it can be figured out by try and error. However, it is complicated for tricyclic graphs. This paper proposes path contraction carrying weights (PCCWs) algorithms to compute the subtree number index for the nontrivial case of bicyclic graphs and all 15 cases of tricyclic graphs, based on three techniques: PCCWs, generating function and structural decomposition. Our approach provides a foundation and useful methods to compute subtree number index for graphs with more complicated cycle structures and can be applied to investigate the novel structural property of some important nanomaterials such as the pentagonal carbon nanocone.

North and South

2008 ◽  
Author(s):  
Elizabeth Gaskell ◽  
Sally Shuttleworth
Keyword(s):  
Middle Class ◽  
Difficult Problem ◽  
The Novel ◽  
Social Authority ◽  
Industrial Town ◽  
Middle Class Woman ◽  
Class Woman ◽  
And Gender ◽  
North And South ◽  
Obedience To Authority

`She tried to settle that most difficult problem for women, how much was to be utterly merged in obedience to authority, and how much might be set apart for freedom in working.’ North and South is a novel about rebellion. Moving from the industrial riots of discontented millworkers through to the unsought passions of a middle-class woman, and from religious crises of conscience to the ethics of naval mutiny, it poses fundamental questions about the nature of social authority and obedience. Through the story of Margaret Hale, the middle-class southerner who moves to the northern industrial town of Milton, Gaskell skilfully explores issues of class and gender in the conflict between Margaret’s ready sympathy with the workers and her growing attraction to the charismatic mill ownder, John Thornton. This new revised and expanded edition sets the novel in the context of Victorian social and medical debate.

Maximum total irregularity index of some families of graph with maximum degree n − 1

2021 ◽  
pp. 2250069
Author(s):  
Shamaila Yousaf ◽  
Akhlaq Ahmad Bhatti
Keyword(s):  
Maximum Degree ◽  
Discrete Math ◽  
Simple Approach ◽  
Unicyclic Graphs ◽  
Irregularity Index ◽  
Degree Of A Vertex ◽  
Tricyclic Graphs ◽  
Bicyclic Graphs ◽  
Appl Math

The total irregularity index of a graph [Formula: see text] is defined by Abdo et al. [H. Abdo, S. Brandt and D. Dimitrov, The total irregularity of a graph, Discrete Math. Theor. Comput. Sci. 16 (2014) 201–206] as [Formula: see text], where [Formula: see text] denotes the degree of a vertex [Formula: see text]. In 2014, You et al. [L. H. You, J. S. Yang and Z. F. You, The maximal total irregularity of unicyclic graphs, Ars Comb. 114 (2014) 153–160.] characterized the graph having maximum [Formula: see text] value among all elements of the class [Formula: see text] (Unicyclic graphs) and Zhou et al. [L. H. You, J. S. Yang, Y. X. Zhu and Z. F. You, The maximal total irregularity of bicyclic graphs, J. Appl. Math. 2014 (2014) 785084, http://dx.doi.org/10.1155/2014/785084 ] characterized the graph having maximum [Formula: see text] value among all elements of the class [Formula: see text] (Bicyclic graphs). In this paper, we characterize the aforementioned graphs with an alternative but comparatively simple approach. Also, we characterized the graphs having maximum [Formula: see text] value among the classes [Formula: see text] (Tricyclic graphs), [Formula: see text] (Tetracyclic graphs), [Formula: see text] (Pentacyclic graphs) and [Formula: see text] (Hexacyclic graphs).

scholarly journals Expedited Biodegradation of Organic Pollutants and Refractory Compounds Using Bio-Electrochemical Systems

2021 ◽  
Author(s):  
Eustace Fernando ◽  
Godfrey Kyazze ◽  
Ahmed Ahsan ◽  
Pavithra Fernando
Keyword(s):  
Difficult Problem ◽  
The Novel ◽  
Alternative Technologies ◽  
Electrochemical Systems ◽  
Novel Technology ◽  
Refractory Compounds ◽  
Slow Kinetics ◽  
Rapid Removal ◽  
High Level ◽  
Kinetics Of

Biodegradation of xenobiotics is often considered to be a slow process. This is especially true if the xenobiotic in question is polymeric in nature, contains many chemical substituent groups or generally exhibits high level of toxicity to environmental microbiota. Due to this observed slow kinetics of degradation, removal of many xenobiotics from contaminated environments using conventional bioremediation technologies is a difficult problem. To alleviate this, alternative technologies showing improved kinetics of biodegradation are sought by the scientific community. One such promising approach is the usage of the novel technology of bio-electrochemical systems for improved degradation of xenobiotics. Due to the newness of this technology and affiliated methods, not much information about its usage for biodegradation of xenobiotics is available in literature. Therefore, this chapter aims to address that gap and bring about a comprehensive analysis on the usage of bio-electrochemical systems for rapid removal of xenobiotic contaminants from the environment.

scholarly journals Manifestations of the archetype water as border markers in the novel by M.Yu. Lermontov's "Hero of our time"

2020 ◽  
pp. 33-39
Author(s):  
Yana Pogrebnaya
Keyword(s):  
Generating Function ◽  
Original Version ◽  
Art World ◽  
The Novel ◽  
New Meanings ◽  
The Everyday ◽  
Artistic Interpretation ◽  
Artistic Images ◽  
The Individual

The possibility of identifying different artistic images that are correlated with a single version of water, and decoding the meaning of these invariant manifestations of the original version in the art world M.Yu. Lermontov is determined by two circumstances: firstly, the objectively existing universal significance of the water archetype as infinitely generating new meanings and images of the beginning, and secondly, by the individual artistic interpretation of the everyday meanings of the water archetype in the novel by M.Yu. Lermontov's "Hero of our time", significant for understanding the concept of space, approved in the literary world of the novel. The relevance of the study of the manifestations of the archetype "water" is determined by their meaning-generating function in the artistic system of the novel by M.Yu. Lermontov "Hero of our time."

scholarly journals Ordering chemical graphs by Sombor indices and its applications

2021 ◽  
Vol 87 (01) ◽  
pp. 5-22
Author(s):  
Hechao Liu ◽  
◽  
Lihua You ◽  
Yufei Huang
Keyword(s):  
Chemical Properties ◽  
Topological Indices ◽  
Unicyclic Graphs ◽  
Degree Of Vertex ◽  
Numerical Invariants ◽  
Tricyclic Graphs ◽  
Bicyclic Graphs ◽  
Physical And Chemical ◽  
And Chemical Properties ◽  
Chemical Trees

Topological indices are a class of numerical invariants that predict certain physical and chemical properties of molecules. Recently, two novel topological indices, named as Sombor index and reduced Sombor index, were introduced by Gutman, defined as where denotes the degree of vertex in . In this paper, our aim is to order the chemical trees, chemical unicyclic graphs, chemical bicyclic graphs and chemical tricyclic graphs with respect to Sombor index and reduced Sombor index. We determine the first fourteen minimum chemical trees, the first four minimum chemical unicyclic graphs, the first three minimum chemical bicyclic graphs, the first seven minimum chemical tricyclic graphs. At last, we consider the applications of reduced Sombor index to octane isomers.

scholarly journals The A α -spectral radius of complements of bicyclic and tricyclic graphs with n vertices

2021 ◽  
Vol 10 (1) ◽  
pp. 56-66
Author(s):  
Chaohui Chen ◽  
Jiarong Peng ◽  
Tianyuan Chen
Keyword(s):  
Extremal Problem ◽  
Spectral Radius ◽  
Unicyclic Graphs ◽  
Tricyclic Graphs ◽  
Bicyclic Graphs

Abstract Recently, the extremal problem of the spectral radius in the class of complements of trees, unicyclic graphs, bicyclic graphs and tricyclic graphs had been studied widely. In this paper, we extend the largest ordering of A α -spectral radius among all complements of bicyclic and tricyclic graphs with n vertices, respectively.

scholarly journals On matrix models and their q-deformations

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Luca Cassia ◽  
Rebecca Lodin ◽  
Maxim Zabzine
Keyword(s):  
Matrix Models ◽  
Generating Function ◽  
Matrix Model ◽  
Gauge Theories ◽  
Classical Case ◽  
The Novel ◽  
Additional Result ◽  
Expectation Values ◽  
Algebra Representation ◽  
Supersymmetric Gauge

Abstract Motivated by the BPS/CFT correspondence, we explore the similarities be- tween the classical β-deformed Hermitean matrix model and the q-deformed matrix models associated to 3d $$ \mathcal{N} $$ N = 2 supersymmetric gauge theories on D2×qS1 and $$ {S}_b^3 $$ S b 3 by matching parameters of the theories. The novel results that we obtain are the correlators for the models, together with an additional result in the classical case consisting of the W -algebra representation of the generating function. Furthermore, we also obtain surprisingly simple expressions for the expectation values of characters which generalize previously known results.

scholarly journals General Multiplicative Zagreb Indices of Graphs with a Small Number of Cycles

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 514 ◽  
Author(s):  
Monther R. Alfuraidan ◽  
Tomáš Vetrík ◽  
Selvaraj Balachandran
Keyword(s):  
Upper Bounds ◽  
Extremal Graphs ◽  
Lower And Upper Bounds ◽  
Zagreb Indices ◽  
Special Cases ◽  
Tricyclic Graphs ◽  
Bicyclic Graphs ◽  
Number Of Cycles

We present lower and upper bounds on the general multiplicative Zagreb indices for bicyclic graphs of a given order and number of pendant vertices. Then, we generalize our methods and obtain bounds for the general multiplicative Zagreb indices of tricyclic graphs, tetracyclic graphs and graphs of given order, size and number of pendant vertices. We show that all our bounds are sharp by presenting extremal graphs including graphs with symmetries. Bounds for the classical multiplicative Zagreb indices are special cases of our results.

The novel steroidal glycoside from the dried bulb of Allium Macrostemon Bunge inhibits platelet activation

2010 ◽  
Vol 34 (8) ◽  
pp. S33-S33
Author(s):  
Wenchao Ou ◽  
Haifeng Chen ◽  
Yun Zhong ◽  
Benrong Liu ◽  
Keji Chen
Keyword(s):  
Platelet Activation ◽  
The Novel ◽  
Steroidal Glycoside ◽  
Allium Macrostemon
Sign in / Sign up

Export Citation Format

Share Document