scholarly journals On investigations of graphs preserving the Wiener index upon vertex removal

2021 ◽  
Vol 6 (12) ◽  
pp. 12976-12985
Author(s):  
Yi Hu ◽  
◽  
Zijiang Zhu ◽  
Pu Wu ◽  
Zehui Shao ◽  
...  
Keyword(s):  
Wiener Index ◽  
Open Problems ◽  
Vertex Removal

<abstract><p>In this paper, we present solutions of two open problems regarding the Wiener index $ W(G) $ of a graph $ G $. More precisely, we prove that for any $ r \geq 2 $, there exist infinitely many graphs $ G $ such that $ W(G) = W(G - \{v_1, \ldots, v_r\}) $, where $ v_1, \ldots, v_r $ are $ r $ distinct vertices of $ G $. We also prove that for any $ r \geq 1 $ there exist infinitely many graphs $ G $ such that $ W(G) = W(G - \{v_i\}) $, $ 1 \leq i \leq r $, where $ v_1, \ldots, v_r $ are $ r $ distinct vertices of $ G $.</p></abstract>

Graphs preserving Wiener index upon vertex removal

2018 ◽  
Vol 338 ◽  
pp. 25-32
Author(s):  
Martin Knor ◽  
Snježana Majstorović ◽  
Riste Škrekovski
Keyword(s):  
Wiener Index ◽  
Vertex Removal

scholarly journals Extremal Values of Ratios: Distance Problems vs. Subtree Problems in Trees

10.37236/3020 ◽  
2013 ◽  
Vol 20 (1) ◽  
Author(s):  
László Székely ◽  
Hua Wang
Keyword(s):  
Negative Correlation ◽  
Wiener Index ◽  
Extremal Problems ◽  
Open Problems ◽  
Extremal Values ◽  
Appl Math

The authors discovered a dual behaviour of two tree indices, the Wiener index and the number of subtrees, for a number of extremal problems  [Discrete Appl. Math. 155 (3) 2006, 374-385;  Adv. Appl. Math. 34 (2005), 138-155]. Barefoot, Entringer and Székely [Discrete Appl. Math. 80 (1997), 37-56] determined extremal values of $\sigma_T(w)/\sigma_T(u)$,   $\sigma_T(w)/\sigma_T(v)$, $\sigma(T)/\sigma_T(v)$, and $\sigma(T)/\sigma_T(w)$, where $T$ is a tree on $n$ vertices, $v$ is in the centroid of the tree $T$, and $u,w$ are leaves in $T$.In this paper  we test how far the negative correlation between distances and subtrees go if we look for the   extremal values of $F_T(w)/F_T(u)$, $F_T(w)/F_T(v)$, $F(T)/F_T(v)$, and $F(T)/F_T(w)$, where $T$ is a tree on $n$ vertices, $v$ is in the subtree core of the tree $T$, and $u,w$ are leaves in $T$-the complete analogue of  [Discrete Appl. Math. 80 (1997), 37-56], changing distances to the number of subtrees.  We include a number of open problems, shifting the interest towards the number of subtrees in graphs.

Topics in Quaternion Linear Algebra

2014 ◽  
Author(s):  
Leiba Rodman
Keyword(s):  
Linear Algebra ◽  
Complex Analysis ◽  
Dimensional Space ◽  
Applied Mathematics ◽  
Three Dimensional ◽  
Number System ◽  
Graduate Course ◽  
Open Problems ◽  
Unpublished Research ◽  
Reference Tool

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.

Allelopathic and Medicinal plant. 26. Millettia speciosa

2020 ◽  
Vol 51 (2) ◽  
pp. 125-146
Author(s):  
Nasiruddin Nasiruddin ◽  
Yu Zhangxin ◽  
Ting Zhao Chen Guangying ◽  
Minghui Ji
Keyword(s):  
Community Structure ◽  
Medicinal Plant ◽  
Gel Electrophoresis ◽  
Denaturing Gradient Gel Electrophoresis ◽  
Wiener Index ◽  
Pseudomonas Spp ◽  
Evenness Index ◽  
Gradient Gel Electrophoresis ◽  
Rhizosphere Pseudomonas

We grew cucumber in pots in greenhouse for 9-successive cropping cycles and analyzed the rhizosphere Pseudomonas spp. community structure and abundance by PCR-denaturing gradient gel electrophoresis and quantitative PCR. Results showed that continuous monocropping changed the cucumber rhizosphere Pseudomonas spp. community. The number of DGGE bands, Shannon-Wiener index and Evenness index decreased during the 3rd cropping and thereafter, increased up to the 7th cropping, however, however, afterwards they decreased again. The abundance of Pseudomonas spp. increased up to the 5th successive cropping and then decreased gradually. These findings indicated that the structure and abundance of Pseudomonas spp. community changed with long-term cucumber monocropping, which might be linked to soil sickness caused by its continuous monocropping.

T Wiener Index of Fibonacci Labeled Graph Pn ʘ F4

2018 ◽  
Vol 9 (11) ◽  
pp. 1712-1716
Author(s):  
R. Palanikumar ◽  
A. Rameshkumar
Keyword(s):  
Wiener Index ◽  
Labeled Graph

Wiener index of hexagonal chains under some transformations

2020 ◽  
Vol 3 (1) ◽  
pp. 28-36 ◽  
Author(s):  
Andrey A. Dobrynin ◽  
◽  
Ehsan Estaji ◽  
◽  
Keyword(s):  
Wiener Index

Neurotoxicity of Pesticides: The Roadmap for the Cubic Mode of Action

2020 ◽  
Vol 27 (1) ◽  
pp. 54-77 ◽  
Author(s):  
Bogdan Bumbăcilă ◽  
Mihai V. Putz
Keyword(s):  
Biological Activity ◽  
Wiener Index ◽  
Laboratory Animals ◽  
Covalent Bonds ◽  
Organophosphate Compounds ◽  
Sar Studies ◽  
Structure Activity ◽  
Cubic Structure

Pesticides are used today on a planetary-wide scale. The rising need for substances with this biological activity due to an increasing consumption of agricultural and animal products and to the development of urban areas makes the chemical industry to constantly investigate new molecules or to improve the physicochemical characteristics, increase the biological activities and improve the toxicity profiles of the already known ones. Molecular databases are increasingly accessible for in vitro and in vivo bioavailability studies. In this context, structure-activity studies, by their in silico - in cerebro methods, are used to precede in vitro and in vivo studies in plants and experimental animals because they can indicate trends by statistical methods or biological activity models expressed as mathematical equations or graphical correlations, so a direction of study can be developed or another can be abandoned, saving financial resources, time and laboratory animals. Following this line of research the present paper reviews the Structure-Activity Relationship (SAR) studies and proposes a correlation between a topological connectivity index and the biological activity or toxicity made as a result of a study performed on 11 molecules of organophosphate compounds, randomly chosen, with a basic structure including a Phosphorus atom double bounded to an Oxygen atom or to a Sulfur one and having three other simple covalent bonds with two alkoxy (-methoxy or -ethoxy) groups and to another functional group different from the alkoxy groups. The molecules were packed on a cubic structure consisting of three adjacent cubes, respecting a principle of topological efficiency, that of occupying a minimal space in that cubic structure, a method that was called the Clef Method. The central topological index selected for correlation was the Wiener index, since it was possible this way to discuss different adjacencies between the nodes in the graphs corresponding to the organophosphate compounds molecules packed on the cubic structure; accordingly, &quot;three dimensional&quot; variants of these connectivity indices could be considered and further used for studying the qualitative-quantitative relationships for the specific molecule-enzyme interaction complexes, including correlation between the Wiener weights (nodal specific contributions to the total Wiener index of the molecular graph) and the biochemical reactivity of some of the atoms. Finally, when passing from SAR to Q(uantitative)-SAR studies, especially by the present advanced method of the cubic molecule (Clef Method) and its good assessment of the (neuro)toxicity of the studied molecules and of their inhibitory effect on the target enzyme - acetylcholinesterase, it can be seen that a predictability of the toxicity and activity of different analogue compounds can be ensured, facilitating the in vivo experiments or improving the usage of pesticides.

Continuous Glucose Monitoring Time Series and Hypo/Hyperglycemia Prevention: Requirements, Methods, Open Problems

2008 ◽  
Vol 4 (3) ◽  
pp. 181-192 ◽  
Author(s):  
Giovanni Sparacino ◽  
Andrea Facchinetti ◽  
Alberto Maran ◽  
Claudio Cobelli
Keyword(s):  
Time Series ◽  
Continuous Glucose Monitoring ◽  
Glucose Monitoring ◽  
Open Problems ◽  
Monitoring Time

Secure Cloud Quantum Computing with Verification Based on Quantum Interactive Proof

Impact ◽  
2019 ◽  
Vol 2019 (10) ◽  
pp. 30-32
Author(s):  
Tomoyuki Morimae
Keyword(s):  
Quantum Computing ◽  
Quantum Information ◽  
Theoretical Physics ◽  
View Point ◽  
Research Subjects ◽  
Interactive Proof ◽  
Open Problems ◽  
Main Research ◽  
Proof Systems ◽  
Information Group

In cloud quantum computing, a classical client delegate quantum computing to a remote quantum server. An important property of cloud quantum computing is the verifiability: the client can check the integrity of the server. Whether such a classical verification of quantum computing is possible or not is one of the most important open problems in quantum computing. We tackle this problem from the view point of quantum interactive proof systems. Dr Tomoyuki Morimae is part of the Quantum Information Group at the Yukawa Institute for Theoretical Physics at Kyoto University, Japan. He leads a team which is concerned with two main research subjects: quantum supremacy and the verification of quantum computing.

Classification of Cloud Systems Cyber-security Threats and Solutions Directives

2017 ◽  
Vol 2 (3) ◽  
pp. 1
Author(s):  
Hanane Bennasar ◽  
Mohammad Essaaidi ◽  
Ahmed Bendahmane ◽  
Jalel Benothmane
Keyword(s):  
Cloud Computing ◽  
Cyber Security ◽  
Data Security ◽  
Denial Of Service ◽  
Security Threats ◽  
Huge Number ◽  
Open Problems ◽  
Long Period ◽  
Near Future

Cloud computing cyber security is a subject that has been in top flight for a long period and even in near future. However, cloud computing permit to stock up a huge number of data in the cloud stockage, and allow the user to pay per utilization from anywhere via any terminal equipment. Among the major issues related to Cloud Computing security, we can mention data security, denial of service attacks, confidentiality, availability, and data integrity. This paper is dedicated to a taxonomic classification study of cloud computing cyber-security. With the main objective to identify the main challenges and issues in this field, the different approaches and solutions proposed to address them and the open problems that need to be addressed.

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