Wiener index and addressing of the total graph

2021 ◽  
Vol 51 (4) ◽  
Author(s):  
M. Gholamnia Taleshani ◽  
Ahmad Abbasi
Keyword(s):  
Wiener Index ◽  
Total Graph

Energy and Wiener index of Total Graph over RingZn

2017 ◽  
Vol 63 ◽  
pp. 485-495
Author(s):  
Sheela Suthar ◽  
Om Prakash
Keyword(s):  
Wiener Index ◽  
Total Graph

scholarly journals Some distance based indices of graphs based on four new operations related to the lexicographic product

2019 ◽  
Vol 11 (2) ◽  
pp. 258-267
Author(s):  
N. Dehgardi ◽  
S.M. Sheikholeslami ◽  
M. Soroudi
Keyword(s):  
Molecular Graph ◽  
Wiener Index ◽  
Lexicographic Product ◽  
Total Graph ◽  
Degree Of A Vertex ◽  
Degree Distance

For a (molecular) graph, the Wiener index, hyper-Wiener index and degree distance index are defined as $$W(G)= \sum_{\{u,v\}\subseteq V(G)}d_G(u,v),$$ $$WW(G)=W(G)+\sum_{\{u,v\}\subseteq V(G)} d_{G}(u,v)^2,$$ and $$DD(G)=\sum_{\{u,v\}\subseteq V(G)}d_G(u, v)(d(u/G)+d(v/G)),$$ respectively, where $d(u/G)$ denotes the degree of a vertex $u$ in $G$ and $d_G(u, v)$ is distance between two vertices $u$ and $v$ of a graph $G$. In this paper, we study Wiener index, hyper-Wiener index and degree distance index of graphs based on four new operations related to the lexicographic product, subdivision and total graph.

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

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

scholarly journals Biodiversity of butterflies in endosulfan-affected areas of Kerala, India

2020 ◽  
Vol 81 (1) ◽  
Author(s):  
K. N. Raghavendra ◽  
Kumar Arvind ◽  
G. K. Anushree ◽  
Tony Grace
Keyword(s):  
Monsoon Season ◽  
Winter Season ◽  
Wiener Index ◽  
Long Term Effects ◽  
Affected Area ◽  
Butterfly Assemblages ◽  
Abundance And Diversity ◽  
The One ◽  
One Way Anova

Abstract Background Butterflies are considered as bio-indicators of a healthy and diversified ecosystem. Endosulfan was sprayed indiscriminately in large plantations of Kasaragod district, Kerala which had caused serious threats to the ecosystem. In this study, we surveyed the butterflies for their abundance and diversity in three differentially endosulfan-affected areas viz., Enmakaje—highly affected area, Periye—moderately affected area, Padanakkad—unaffected area, carried out between the end of the monsoon season and the start of the winter season, lasting approximately 100 days. Seven variables viz., butterfly abundance (N), species richness (S), Simpson’s reciprocal index (D), the Shannon–Wiener index (H′), the exponential of the Shannon–Wiener index (expH′), Pielou’s evenness (J) and species evenness (D/S), related to species diversity were estimated, followed by the one-way ANOVA (F = 25.01, p < 0.001) and the Kruskal-Wallis test (H = 22.59, p < 0.001). Results A population of three different butterfly assemblages comprised of 2300 butterflies which represented 61 species were encountered. Our results showed that Enmakaje displayed significantly lower butterfly diversity and abundance, compared to the other two communities. Conclusion So far, this is the first study concerning the effect of endosulfan on the biodiversity of butterfly in the affected areas of Kasaragod, Kerala, India. This study may present an indirect assessment of the persisting effects of endosulfan in the affected areas, suggesting its long-term effects on the ecosystem.

scholarly journals On Structure Descriptors Related with Intramolecular Energy of Alkanes

2004 ◽  
Vol 59 (10) ◽  
pp. 694-698 ◽  
Author(s):  
Ivan Gutman ◽  
Boris Furtula ◽  
Biljana Arsić
Keyword(s):  
Organic Molecule ◽  
Wiener Index ◽  
Critical Value ◽  
Fixed Number ◽  
Methyl Groups ◽  
Parallel Lines ◽  
Analytical Expressions

In an earlier work it was demonstrated that the Zenkevich index U provides a measure of the intramolecular energy of an organic molecule, and that - in the case of alkanes - it is related to the Wiener index. We now show that U is much closer related to the recently introduced variable Wiener index Wλ : Within sets of isomeric alkanes, the relation between U and Wλ is linear, the (U,Wλ )-points forming several, mutually parallel, lines. Each such line pertains to a group of isomers possessing a fixed number of methyl groups. There exists a critical value of the parameter λ for which all the (U,Wλ )-lines coalesce, in which case the relation between U and Wλ becomes independent of the number of methyl groups. Approximate analytical expressions for the (U,Wλ )-dependence are deduced.

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