The Average Wiener Index of Trees and Chemical Trees

1999 ◽  
Vol 39 (4) ◽  
pp. 679-683 ◽  
Author(s):  
Andrey A. Dobrynin ◽  
Ivan Gutman
Keyword(s):  
Wiener Index ◽  
Chemical Trees

A Linear Algorithm for the Hyper-Wiener Index of Chemical Trees

2001 ◽  
Vol 41 (4) ◽  
pp. 958-963 ◽  
Author(s):  
Roberto Aringhieri ◽  
Pierre Hansen ◽  
Federico Malucelli
Keyword(s):  
Wiener Index ◽  
Linear Algorithm ◽  
Chemical Trees

Extremal trees with respect to the Steiner Wiener index

2019 ◽  
Vol 11 (06) ◽  
pp. 1950067
Author(s):  
Jie Zhang ◽  
Guang-Jun Zhang ◽  
Hua Wang ◽  
Xiao-Dong Zhang
Keyword(s):  
Maximum Degree ◽  
Computational Analysis ◽  
Degree Sequence ◽  
Wiener Index ◽  
Extremal Problems ◽  
Difficult Problem ◽  
Computational Results ◽  
Number Of Leaves ◽  
Extremal Structure ◽  
Chemical Trees

The well-known Wiener index is defined as the sum of pairwise distances between vertices. Extremal problems with respect to it have been extensively studied for trees. A generalization of the Wiener index, called the Steiner Wiener index, takes the sum of minimum sizes of subgraphs that span [Formula: see text] given vertices over all possible choices of the [Formula: see text] vertices. We consider the extremal problems with respect to the Steiner Wiener index among trees of a given degree sequence. First, it is pointed out minimizing the Steiner Wiener index in general may be a difficult problem, although the extremal structure may very likely be the same as that for the regular Wiener index. We then consider the upper bound of the general Steiner Wiener index among trees of a given degree sequence and study the corresponding extremal trees. With these findings, some further discussion and computational analysis are presented for chemical trees. We also propose a conjecture based on the computational results. In addition, we identify the extremal trees that maximize the Steiner Wiener index among trees with a given maximum degree or number of leaves.

scholarly journals Extremal Chemical Trees

2002 ◽  
Vol 57 (1-2) ◽  
pp. 49-51
Author(s):  
Miranca Fischermann ◽  
Ivan Gutman ◽  
Arne Hoffmann ◽  
Dieter Rautenbach ◽  
Dušica Vidovića ◽  
...  
Keyword(s):  
Carbon Atom ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Wiener Index ◽  
Graph Representation ◽  
Hosoya Index ◽  
Saturated Hydrocarbons ◽  
Physico Chemical ◽  
Graph Energy ◽  
Chemical Trees

A variety of molecular-graph-based structure-descriptors were proposed, in particular the Wiener index W. the largest graph eigenvalue λ1, the connectivity index X, the graph energy E and the Hosoya index Z, capable of measuring the branching of the carbon-atom skeleton of organic compounds, and therefore suitable for describing several of their physico-chemical properties. We now determine the structure of the chemical trees (= the graph representation of acyclic saturated hydrocarbons) that are extremal with respect to W , λ1, E, and Z. whereas the analogous problem for X was solved earlier. Among chemical trees with 5. 6, 7, and 3k + 2 vertices, k = 2,3,..., one and the same tree has maximum λ1 and minimum W, E, Z. Among chemical trees with 3k and 3k +1 vertices, k = 3,4...., one tree has minimum 11 and maximum λ1 and another minimum E and Z .

Extremal Chemical Trees

2002 ◽  
Vol 57 (9-10) ◽  
pp. 49-52 ◽  
Author(s):  
Miranca Fischermann ◽  
Ivan Gutmana ◽  
Arne Hoffmann ◽  
Dieter Rautenbach ◽  
Dušica Vidović ◽  
...  
Keyword(s):  
Carbon Atom ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Wiener Index ◽  
Graph Representation ◽  
Hosoya Index ◽  
Saturated Hydrocarbons ◽  
Physico Chemical ◽  
Graph Energy ◽  
Chemical Trees

Avariety of molecular-graph-based structure-descriptors were proposed, in particular the Wiener index W, the largest graph eigenvalue λ1, the connectivity index χ, the graph energy E and the Hosoya index Z, capable of measuring the branching of the carbon-atom skeleton of organic compounds, and therefore suitable for describing several of their physico-chemical properties. We now determine the structure of the chemical trees (= the graph representation of acyclic saturated hydrocarbons) that are extremal with respect to W, λ1, E, and Z, whereas the analogous problem for χ was solved earlier. Among chemical trees with 5, 6, 7, and 3k + 2 vertices, k = 2, 3,..., one and the same tree has maximum λ1 and minimum W, E, Z. Among chemical trees with 3k and 3k + 1 vertices, k = 3, 4..., one tree has minimum W and maximum λ1 and another minimum E and Z.

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, "three dimensional" 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.

scholarly journals The structure of graphs with given number of blocks and the maximum Wiener index

2019 ◽  
Vol 39 (1) ◽  
pp. 170-184 ◽  
Author(s):  
Stéphane Bessy ◽  
François Dross ◽  
Katarína Hriňáková ◽  
Martin Knor ◽  
Riste Škrekovski
Keyword(s):  
Wiener Index
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