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.

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.

scholarly journals M-Polynomials and Associated Topological Indices of Sodalite Materials

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ghazanfar Abbas ◽  
Muhammad Ibrahim ◽  
Ali Ahmad ◽  
Muhammad Azeem ◽  
Kashif Elahi
Keyword(s):  
Greenhouse Gases ◽  
Topological Index ◽  
Low Cost ◽  
Chemical Properties ◽  
Topological Indices ◽  
Mathematical Tool ◽  
Physical And Chemical Properties ◽  
Natural Zeolites ◽  
Physical And Chemical ◽  
And Chemical Properties

Natural zeolites are commonly described as macromolecular sieves. Zeolite networks are very trendy chemical networks due to their low-cost implementation. Sodalite network is one of the most studied types of zeolite networks. It helps in the removal of greenhouse gases. To study this rich network, we use an authentic mathematical tool known as M-polynomials of the topological index and show some physical and chemical properties in numerical form, and to understand the structure deeply, we compare different legitimate M-polynomials of topological indices, concluding in the form of graphical comparisons.

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.

scholarly journals Some Topological Measures for Nicotine

2020 ◽  
pp. 287-296
Author(s):  
Abaid ur Rehman Virk
Keyword(s):  
Topological Index ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Physical And Chemical Properties ◽  
Quantitative Structure ◽  
Structure Property ◽  
Structure Property Relationship ◽  
Topological Measures ◽  
Physical And Chemical ◽  
And Chemical Properties

A topological index is a quantity expressed as a number that help us to catch symmetry of chemical compounds. With the help of quantitative structure property relationship (QSPR), we can guess physical and chemical properties of several chemical compounds. Here, we will compute Shingali & Kanabour, Gourava and hype Gourava indices for the chemical compound Nicotine.

scholarly journals Computing Bounds for Second Zagreb Coindex of Sum Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Muhammad Javaid ◽  
Muhammad Ibraheem ◽  
Uzma Ahmad ◽  
Q. Zhu
Keyword(s):  
Computer Science ◽  
Cartesian Product ◽  
Chemical Properties ◽  
Topological Indices ◽  
Zagreb Indices ◽  
Graph Theoretic ◽  
Cartesian Product Of Graphs ◽  
The Subject ◽  
Product Of Graphs ◽  
And Chemical Properties

Topological indices or coindices are one of the graph-theoretic tools which are widely used to study the different structural and chemical properties of the under study networks or graphs in the subject of computer science and chemistry, respectively. For these investigations, the operations of graphs always played an important role for the study of the complex networks under the various topological indices or coindices. In this paper, we determine bounds for the second Zagreb coindex of a well-known family of graphs called F -sum ( S -sum, R -sum, Q -sum, and T -sum) graphs in the form of Zagreb indices and coindices of their factor graphs, where these graphs are obtained by using four subdivision-related operations and Cartesian product of graphs. At the end, we illustrate the obtained results by providing the exact and bonded values of some specific F -sum graphs.

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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