scholarly journals Calculating degree-based topological indices of dominating David derived networks

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 1015-1021 ◽  
Author(s):  
Muhammad Saeed Ahmad ◽  
Waqas Nazeer ◽  
Shin Min Kang ◽  
Muhammad Imran ◽  
Wei Gao
Keyword(s):  
Chemical Reaction ◽  
Real World ◽  
Network Theory ◽  
Applied Mathematics ◽  
Reaction Network ◽  
Topological Indices ◽  
Theoretical Chemistry ◽  
Mathematical Structures ◽  
Real World Problems ◽  
Chemical Reaction Network Theory

AbstractAn important area of applied mathematics is the Chemical reaction network theory. The behavior of real world problems can be modeled by using this theory. Due to applications in theoretical chemistry and biochemistry, it has attracted researchers since its foundation. It also attracts pure mathematicians because it involves interesting mathematical structures. In this report, we compute newly defined topological indices, namely, Arithmetic-Geometric index (AG1index),SKindex,SK1index, andSK2index of the dominating David derived networks [1, 2, 3, 4, 5].

scholarly journals On Some New Neighborhood Degree-Based Indices for Some Oxide and Silicate Networks

J ◽  
2019 ◽  
Vol 2 (3) ◽  
pp. 384-409
Author(s):  
Sourav Mondal ◽  
Nilanjan De ◽  
Anita Pal
Keyword(s):  
Molecular Structure ◽  
Network Theory ◽  
Topological Index ◽  
Applied Mathematics ◽  
Reaction Network ◽  
Topological Indices ◽  
Zagreb Index ◽  
Second Zagreb Index ◽  
Real World Problems ◽  
Chemical Reaction Network Theory

Topological indices are numeric quantities that describes the topology of molecular structure in mathematical chemistry. An important area of applied mathematics is the chemical reaction network theory. Real-world problems can be modeled using this theory. Due to its worldwide applications, chemical networks have attracted researchers since their foundation. In this report, some silicate and oxide networks are studied, and exact expressions of some newly-developed neighborhood degree-based topological indices named as the neighborhood Zagreb index ( M N ), the neighborhood version of the forgotten topological index ( F N ), the modified neighborhood version of the forgotten topological index ( F N ∗ ), the neighborhood version of the second Zagreb index ( M 2 ∗ ), and neighborhood version of the hyper Zagreb index ( H M N ) are obtained for the aforementioned networks. In addition, a comparison among all the indices is shown graphically.

scholarly journals Neighbourhood Degree – Based Topological Indices of Graphene Structure

2021 ◽  
Vol 11 (5) ◽  
pp. 13681-13694
Keyword(s):  
Chemical Reaction ◽  
Real World ◽  
Research Area ◽  
Chemical Reaction Networks ◽  
Topological Indices ◽  
Reaction Networks ◽  
Mathematical Structures ◽  
Randic Index ◽  
Graphene Structures ◽  
3D Representations

The theory of chemical reaction networks is a branch of mathematics that aims to mimic real-world behavior. This research area has drawn many researchers' attention, primarily due to its biological and empirical chemistry applications. The fascinating problems that emerge from the mathematical structures involved have kindled the interest of pure mathematicians. In this paper, we estimate a few topological indices such as SK index, SK1 index, SK2 index, Modified Randić index, and Inverse Sum Index for the Graphene structure based on the neighborhood degree and obtain results based on both sum and products of the cardinality of edge partitions corresponding to 4 different Graphene structures. We also present the 3D representations of the indices using MATLAB.

scholarly journals An algorithm for building and integrating dynamic systems based on reaction networks

2021 ◽  
Vol 8 (1) ◽  
pp. 49
Author(s):  
Petar Chernev
Keyword(s):  
Chemical Reaction ◽  
Dynamic Systems ◽  
Network Theory ◽  
Dynamic Models ◽  
Reaction Network ◽  
Chemical Reaction Network ◽  
Reaction Networks ◽  
Complex Interactions ◽  
Model Complex ◽  
Chemical Reaction Network Theory

In the present work we give an overview and implementation of an algorithm for building and integrating dynamic systems from reaction networks. Reaction networks have their roots in chemical reaction network theory, but their nature is general enough that they can be applied in many fields to model complex interactions. Our aim is to provide a simple to use program that allows for quick prototyping of dynamic models based on a system of reactions. After introducing the concept of a reaction and a reaction network in a general way, not necessarily connected to chemistry, we outlay the algorithm for building its associated system of ODEs. Finally, we give a few example usages where we examine a range of growth-decay models in the context of reaction networks.

scholarly journals Using chemical reaction network theory to show stability of distributional dynamics in game theory

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ross Cressman ◽  
Vlastimil Křivan
Keyword(s):  
Game Theory ◽  
Chemical Reaction ◽  
Network Theory ◽  
Group Formation ◽  
Evolutionary Game ◽  
Reaction Network ◽  
Chemical Reaction Network ◽  
Positive Equilibrium ◽  
Distributional Dynamics ◽  
Chemical Reaction Network Theory

<p style='text-indent:20px;'>This article shows how to apply results of chemical reaction network theory (CRNT) to prove uniqueness and stability of a positive equilibrium for pairs/groups distributional dynamics that arise in game theoretic models. Evolutionary game theory assumes that individuals accrue their fitness through interactions with other individuals. When there are two or more different strategies in the population, this theory assumes that pairs (groups) are formed instantaneously and randomly so that the corresponding pairs (groups) distribution is described by the Hardy–Weinberg (binomial) distribution. If interactions times are phenotype dependent the Hardy-Weinberg distribution does not apply. Even if it becomes impossible to calculate the pairs/groups distribution analytically we show that CRNT is a general tool that is very useful to prove not only existence of the equilibrium, but also its stability. In this article, we apply CRNT to pair formation model that arises in two player games (e.g., Hawk-Dove, Prisoner's Dilemma game), to group formation that arises, e.g., in Public Goods Game, and to distribution of a single population in patchy environments. We also show by generalizing the Battle of the Sexes game that the methodology does not always apply.</p>

Sign in / Sign up

Export Citation Format

Share Document