Application of Corona Product of Graphs in Computing Topological Indices of Some Special Chemical Graphs

2017 ◽  
pp. 82-101
Author(s):  
Nilanjan De
Keyword(s):  
Topological Indices ◽  
Connectivity Index ◽  
Eccentric Connectivity Index ◽  
Molecular Graphs ◽  
Mathematical Chemistry ◽  
Graph Operations ◽  
Eccentricity Index ◽  
Chemical Graphs ◽  
Product Of Graphs ◽  
Corona Product

Graph operations play a very important role in mathematical chemistry, since some chemically interesting graphs can be obtained from some simpler graphs by different graph operations. In this chapter, some eccentricity based topological indices such as the total eccentricity index, eccentric connectivity index, modified eccentric connectivity index and connective eccentricity index and their respective polynomial versions of corona product of two graphs have been studied and also these indices of some important classes of chemically interesting molecular graphs are determined by specializing the components of corona product of graphs.

scholarly journals On Eccentricity-Based Topological Indices and Polynomials of Phosphorus Containing Dendrimers

2018 ◽  
Author(s):  
Shin Min Kang ◽  
Zahid Iqbal ◽  
Muhammad Ishaq ◽  
Rabia Sarfraz ◽  
Adnan Aslam ◽  
...  
Keyword(s):  
Topological Indices ◽  
Connectivity Index ◽  
The Other ◽  
Topological Descriptors ◽  
Eccentric Connectivity Index ◽  
Important Place ◽  
Eccentricity Index ◽  
Phosphorus Containing ◽  
Pharmaceutical Properties ◽  
High Degree

In the study of QSAR/QSPR, due to high degree of predictability of pharmaceutical properties, the eccentric-connectivity index has very important place among the other topological descriptors, In this paper, we compute the exact formulas of eccentric-connectivity index and its corresponding polynomial, total eccentric-connectivity index and its corresponding polynomial, first Zagreb eccentricity index, augmented eccentric-connectivity index, modified eccentric-connectivity index and its corresponding polynomial for a class of phosphorus containing dendrimers.

scholarly journals Eccentric Connectivity and Zagreb Coindices of the Generalized Hierarchical Product of Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
M. Tavakoli ◽  
F. Rahbarnia ◽  
A. R. Ashrafi
Keyword(s):  
Connectivity Index ◽  
Explicit Formulas ◽  
Eccentric Connectivity Index ◽  
Chemical Graphs ◽  
Product Of Graphs

Formulas for calculations of the eccentric connectivity index and Zagreb coindices of graphs under generalized hierarchical product are presented. As an application, explicit formulas for eccentric connectivity index and Zagreb coindices of some chemical graphs are obtained.

scholarly journals Eccentric topological properties of a graph associated to a finite dimensional vector space

2020 ◽  
Vol 43 (1) ◽  
pp. 164-176
Author(s):  
Jia-Bao Liu ◽  
Imran Khalid ◽  
Mohammad Tariq Rahim ◽  
Masood Ur Rehman ◽  
Faisal Ali ◽  
...  
Keyword(s):  
Vector Space ◽  
Topological Index ◽  
Topological Indices ◽  
Connectivity Index ◽  
Dimensional Vector ◽  
Eccentric Connectivity Index ◽  
Dimensional Vector Space ◽  
Eccentricity Index ◽  
Finite Dimensional Vector Space ◽  
Finite Dimensional

AbstractA topological index is actually designed by transforming a chemical structure into a number. Topological index is a graph invariant which characterizes the topology of the graph and remains invariant under graph automorphism. Eccentricity based topological indices are of great importance and play a vital role in chemical graph theory. In this article, we consider a graph (non-zero component graph) associated to a finite dimensional vector space over a finite filed in the context of the following eleven eccentricity based topological indices: total eccentricity index; average eccentricity index; eccentric connectivity index; eccentric distance sum index; adjacent distance sum index; connective eccentricity index; geometric arithmetic index; atom bond connectivity index; and three versions of Zagreb indices. Relationship of the investigated indices and their dependency with respect to the involved parameters are also visualized by evaluating them numerically and by plotting their results.

scholarly journals Computing Eccentricity-Based Topological Indices of 2-Power Interconnection Networks

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Muhammad Imran ◽  
Muhammad Azhar Iqbal ◽  
Yun Liu ◽  
Abdul Qudair Baig ◽  
Waqas Khalid ◽  
...  
Keyword(s):  
Topological Structure ◽  
Interconnection Networks ◽  
Interconnection Network ◽  
Topological Indices ◽  
Connectivity Index ◽  
Eccentric Connectivity Index ◽  
Zagreb Index ◽  
Eccentricity Index ◽  
Computer Scientists ◽  
Partition Method

In a connected graph G with a vertex v, the eccentricity εv of v is the distance between v and a vertex farthest from v in the graph G. Among eccentricity-based topological indices, the eccentric connectivity index, the total eccentricity index, and the Zagreb index are of vital importance. The eccentric connectivity index of G is defined by ξG = ∑v∈VGdvεv, where dv is the degree of the vertex v and εv is the eccentricity of v in G. The topological structure of an interconnected network can be modeled by using graph explanation as a tool. This fact has been universally accepted and used by computer scientists and engineers. More than that, practically, it has been shown that graph theory is a very powerful tool for designing and analyzing the topological structure of interconnection networks. The topological properties of the interconnection network have been computed by Hayat and Imran (2014), Haynes et al. (2002), and Imran et al. (2015). In this paper, we compute the close results for eccentricity-based topological indices such as the eccentric connectivity index, the total eccentricity index, and the first, second, and third Zagreb eccentricity index of a hypertree, sibling tree, and X-tree for k-level by using the edge partition method.

scholarly journals Eccentricity-Based Topological Invariants of Some Chemical Graphs

Atoms ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 21 ◽  
Author(s):  
Nazeran Idrees ◽  
Muhammad Saif ◽  
Tehmina Anwar
Keyword(s):  
Boiling Point ◽  
Topological Index ◽  
Chemical Reactivity ◽  
Topological Indices ◽  
Topological Invariants ◽  
Circulant Graphs ◽  
Eccentric Connectivity Index ◽  
Molecular Graphs ◽  
Eccentricity Index ◽  
Physical And Chemical

Topological index is an invariant of molecular graphs which correlates the structure with different physical and chemical invariants of the compound like boiling point, chemical reactivity, stability, Kovat’s constant etc. Eccentricity-based topological indices, like eccentric connectivity index, connective eccentric index, first Zagreb eccentricity index, and second Zagreb eccentricity index were analyzed and computed for families of Dutch windmill graphs and circulant graphs.

On eccentricity-based topological descriptors of water-soluble dendrimers

2018 ◽  
Vol 74 (1-2) ◽  
pp. 25-33 ◽  
Author(s):  
Zahid Iqbal ◽  
Muhammad Ishaq ◽  
Adnan Aslam ◽  
Wei Gao
Keyword(s):  
Molecular Structure ◽  
Chemical Properties ◽  
Topological Indices ◽  
Water Soluble ◽  
Connectivity Index ◽  
Topological Descriptors ◽  
Physical And Chemical Properties ◽  
Eccentric Connectivity Index ◽  
Physical And Chemical ◽  
And Chemical Properties

AbstractPrevious studies show that certain physical and chemical properties of chemical compounds are closely related with their molecular structure. As a theoretical basis, it provides a new way of thinking by analyzing the molecular structure of the compounds to understand their physical and chemical properties. The molecular topological indices are numerical invariants of a molecular graph and are useful to predict their bioactivity. Among these topological indices, the eccentric-connectivity index has a prominent place, because of its high degree of predictability of pharmaceutical properties. In this article, we compute the closed formulae of eccentric-connectivity–based indices and its corresponding polynomial for water-soluble perylenediimides-cored polyglycerol dendrimers. Furthermore, the edge version of eccentric-connectivity index for a new class of dendrimers is determined. The conclusions we obtained in this article illustrate the promising application prospects in the field of bioinformatics and nanomaterial engineering.

scholarly journals HF-Index and Y-Index of Some New Graph of Operations

2022 ◽  
pp. 28-33
Author(s):  
Dr. S. Nagarajan ◽  
◽  
G. Kayalvizhi ◽  
G. Priyadharsini ◽  
◽  
...  
Keyword(s):  
Cartesian Product ◽  
Graph Operations ◽  
Join Of Graphs ◽  
Product Of Graphs ◽  
Corona Product

In this paper we derive HF index of some graph operations containing join, Cartesian Product, Corona Product of graphs and compute the Y index of new operations of graphs related to the join of graphs.

scholarly journals Vertex-Based Topological Indices of Double and Strong Double Graph of Dutch Windmill Graph

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Muhammad Asad Ali ◽  
Muhammad Shoaib Sardar ◽  
Imran Siddique ◽  
Dalal Alrowaili
Keyword(s):  
Graph Theory ◽  
Chemical Properties ◽  
Topological Indices ◽  
Connectivity Index ◽  
Vaporization Enthalpy ◽  
Zagreb Index ◽  
Graph Operations ◽  
Big Graphs ◽  
Physical And Chemical ◽  
Atom Bond

A measurement of the molecular topology of graphs is known as a topological index, and several physical and chemical properties such as heat formation, boiling point, vaporization, enthalpy, and entropy are used to characterize them. Graph theory is useful in evaluating the relationship between various topological indices of some graphs derived by applying certain graph operations. Graph operations play an important role in many applications of graph theory because many big graphs can be obtained from small graphs. Here, we discuss two graph operations, i.e., double graph and strong double graph. In this article, we will compute the topological indices such as geometric arithmetic index GA , atom bond connectivity index ABC , forgotten index F , inverse sum indeg index ISI , general inverse sum indeg index ISI α , β , first multiplicative-Zagreb index PM 1   and second multiplicative-Zagreb index PM 2 , fifth geometric arithmetic index GA 5 , fourth atom bond connectivity index ABC 4 of double graph, and strong double graph of Dutch Windmill graph D 3 p .

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