Extremal (n,m)-Graphs w.r.t General Multiplicative Zagreb Indices

2020 ◽  
Vol 23 ◽  
Author(s):  
Aisha Javed ◽  
Muhammad Kamran Jamil ◽  
Jia-Bao Liu ◽  
Akbar Ali
Keyword(s):  
Molecular Graph ◽  
Chemical Properties ◽  
Physical And Chemical Properties ◽  
Extremal Graphs ◽  
Unified Approach ◽  
Zagreb Indices ◽  
Graph Transformations ◽  
Bicyclic Graphs ◽  
Physical And Chemical ◽  
And Chemical Properties

Background:: A topological index of a molecular graph is the numeric quantity which can predict certain physical and chemical properties of the corresponding molecule. Xu et al. introduced some graph transformations which increase or decrease the first and second multiplicative Zagreb indices and proposed a unified approach to characterize extremal (n, m)- graphs. Method:: Graph transformations are used to find the extremal graphs, these transformations either increase or decrease the general multiplicative Zagreb indices. By applying the transformations which increase the general multiplicative Zagreb indices we find the graphs with maximal general multiplicative Zagreb indices and for minimal general Zagreb indices we use the transformations which decrease the index. Result:: In this paper, we extend the Xu’s results and show that the same graph transformations increase or decrease the first and second general multiplicative Zagreb indices for . As an application, the extremal acyclic, unicyclic and bicyclic graphs are presented for general multiplicative Zagreb indices. Conclusion:: By applying the transformation we investigated that in the class of acyclic, unicyclic and bicyclic graphs, which graph gives the minimum and the maximum general multiplicative Zagreb indices.

Graph Indices for Cartesian Product of F-sum of Connected Graphs

2021 ◽  
Vol 24 ◽  
Author(s):  
Jia-Bao Liu ◽  
Muhammad Imran ◽  
Shakila Baby ◽  
Hafiz Muhammad Afzal Siddiqui ◽  
Muhammad Kashif Shafiq
Keyword(s):  
Computer Science ◽  
Topological Index ◽  
Cartesian Product ◽  
Chemical Properties ◽  
Physical And Chemical Properties ◽  
Finite Graphs ◽  
Zagreb Indices ◽  
Physical And Chemical ◽  
Minimum Degrees ◽  
And Chemical Properties

Background: A topological index is a real number associated to a graph, that provides information about its physical and chemical properties along with their correlations.Topological indices are being used successfully in Chemistry, Computer Science and many other fields. Aim and Objective: In this article, we apply the well known, Cartesian product on F-sums of connected and finite graphs. We formulate sharp limits for some famous degree dependent indies. Results: Zagreb indices for the graph operations T(G), Q(G), S(G), R(G) and their F-sums have been computed. By using orders and sizes of component graphs, we derive bounds for Zagreb indices, F-index and Narumi-Katayana index. Conclusion: The formulation of expressions for the complicated products on F-sums, in terms of simple parameters like maximum and minimum degrees of basic graphs, reduces the computational complexities.

On Extremal Graphs of Degree Distance Index by Using Edge-Grafting Transformations Method

2020 ◽  
Vol 23 ◽  
Author(s):  
Muhammad Imran ◽  
Shehnaz Akhtar ◽  
Uzma Ahmad ◽  
Sarfraz Ahmad ◽  
Ahsan Bilal
Keyword(s):  
Chemical Properties ◽  
Physical And Chemical Properties ◽  
Extremal Graphs ◽  
Graph Invariant ◽  
Degree Of Vertex ◽  
Degree Distance ◽  
Novel Method ◽  
Physical And Chemical ◽  
And Chemical Properties ◽  
Domination Numbers

Background: Topological indices have numerous implementations in chemistry, biology and in lot of other areas. It is a real number associated to a graph, which provides information about its physical and chemical properties and their correlations. For a connected graph H, the degree distance defined as DD(H)=∑_(\h_1,h_2⊆V(H))〖(〖deg〗_H (h_1 )+〖deg〗_H (h_2 )) d_H (h_1,h_2 ) 〗, where 〖deg〗_H (h_1 ) is the degree of vertex h_1and d_H (h_1,h_2 ) is the distance between h_1and h_2in the graph H. Aim and Objective: In this article, we characterize some extremal trees with respect to degree distance index which has a lot of applications in theoretical and computational chemistry. Materials and Methods: A novel method of edge-grafting transformations is used. We discuss the behavior of DD index under four edge-grafting transformations. Results: By the help of those transformations, we derive some extremal trees under certain parameters including pendant vertices, diameter, matching and domination numbers. Some extremal trees for this graph invariant are also characterized. Conclusion: It is shown that balanced spider approaches to the smallest DD index among trees having given fixed leaves. The tree Cn,d has the smallest DD index, among the all trees of diameter d. It is also proved that the matching number and domination numbers are equal for trees having minimum DD index.

scholarly journals Zagreb Polynomials and Redefined Zagreb Indices for Chemical Structures Helpful in the Treatment of COVID-19

2020 ◽  
Vol 4 (4) ◽  
pp. 33-40
Author(s):  
Abaid ur Rehman Virk
Keyword(s):  
Topological Index ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Physical And Chemical Properties ◽  
Zagreb Indices ◽  
Chemical Structures ◽  
Physical And Chemical ◽  
And Chemical Properties

A topological index (TI) is a number that is helpful in predicting the properties of chemical compounds. We can estimate the physical and chemical properties of several chemical compounds. In this study, we compute Zagreb polynomials and the redefined Zagreb indices for chemical compounds used in the treatment of COVID-19 namely remdesivir, chloroquine, hydroxychloroquine and theaflavin.

Statistical criteria of stellar population types

1966 ◽  
Vol 24 ◽  
pp. 101-110
Author(s):  
W. Iwanowska
Keyword(s):  
Stellar Population ◽  
Chemical Properties ◽  
Spectrophotometric Study ◽  
Physical And Chemical Properties ◽  
Population Type ◽  
The Galaxy ◽  
Distribution Parameters ◽  
Physical And Chemical ◽  
Statistical Criteria ◽  
And Chemical Properties

In connection with the spectrophotometric study of population-type characteristics of various kinds of stars, a statistical analysis of kinematical and distribution parameters of the same stars is performed at the Toruń Observatory. This has a twofold purpose: first, to provide a practical guide in selecting stars for observing programmes, second, to contribute to the understanding of relations existing between the physical and chemical properties of stars and their kinematics and distribution in the Galaxy.

Response of corn (Zea mays L.) to various organic-based fertilizers in marginal upland of Sta. Rita, Samar

2017 ◽  
pp. 31-43
Author(s):  
Berta Ratilla ◽  
Loreme Cagande ◽  
Othello Capuno
Keyword(s):  
Block Design ◽  
Management Strategies ◽  
Chemical Properties ◽  
Organic Fertilizers ◽  
Growth And Yield ◽  
Physical And Chemical Properties ◽  
Total N ◽  
Randomized Complete Block Design ◽  
Physical And Chemical ◽  
And Chemical Properties

Organic farming is one of the management strategies that improve productivity of marginal uplands. The study aimed to: (1) evaluate effects of various organic-based fertilizers on the growth and yield of corn; (2) determine the appropriate combination for optimum yield; and (3) assess changes on the soil physical and chemical properties. Experiment was laid out in Randomized Complete Block Design, with 3 replications and 7 treatments, namely; T0=(0-0-0); T1=1t ha-1 Evans + 45-30-30kg N, P2O5, K2O ha-1; T2=t ha-1 Wellgrow + 45-30-30kg N, P2O5, K2O ha-1; T3=15t ha-1 chicken dung; T4=10t ha-1 chicken dung + 45-30-30kg N, P2O5, K2O ha-1; T5=15t ha-1 Vermicast; and T6=10t ha-1 Vermicast + 45-30-30kg N, P2O5, K2O ha-1. Application of organic-based fertilizers with or without inorganic fertilizers promoted growth of corn than the control. But due to high infestation of corn silk beetle(Monolepta bifasciata Horns), its grain yield was greatly affected. In the second cropping, except for Evans, any of these fertilizers applied alone or combined with 45-30-30kg N, P2O5, K2O ha-1 appeared appropriate in increasing corn earyield. Soil physical and chemical properties changed with addition of organic fertilizers. While bulk density decreased irrespective of treatments, pH, total N, available P and exchangeable K generally increased more with chicken dung application.

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