scholarly journals Network Similarity Measure and Ediz Eccentric Connectivity Index

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Guihai Yu ◽  
Xinzhuang Chen
Keyword(s):  
Similarity Measure ◽  
Similarity Measures ◽  
Wiener Index ◽  
Topological Indices ◽  
Connectivity Index ◽  
Laplacian Eigenvalue ◽  
Eccentric Connectivity Index ◽  
Graph Energy ◽  
Network Similarity ◽  
The One

Network similarity measures have proven essential in the field of network analysis. Also, topological indices have been used to quantify the topology of networks and have been well studied. In this paper, we employ a new topological index which we call the Ediz eccentric connectivity index. We use this quantity to define network similarity measures as well. First, we determine the extremal value of the Ediz eccentric connectivity index on some network classes. Second, we compare the network similarity measure based on the Ediz eccentric connectivity index with other well-known topological indices such as Wiener index, graph energy, Randić index, the largest eigenvalue, the largest Laplacian eigenvalue, and connectivity eccentric index. Numerical results underpin the usefulness of the chosen measures. They show that our new measure outperforms all others, except the one based on Wiener index. This means that the measure based on Wiener index is still the best, but the new one has certain advantage to some extent.

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 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.

On the eccentric connectivity index and Wiener index of a graph

2014 ◽  
Vol 37 (1) ◽  
pp. 39-47 ◽  
Author(s):  
P. Dankelmann ◽  
M.J. Morgan ◽  
S. Mukwembi ◽  
H.C. Swart
Keyword(s):  
Wiener Index ◽  
Connectivity Index ◽  
Eccentric Connectivity Index

scholarly journals Topological Descriptors of M-Carbon M r , s , t

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Hong Yang ◽  
Muhammad Naeem
Keyword(s):  
Crystal Structures ◽  
Topological Indices ◽  
Connectivity Index ◽  
Topological Descriptors ◽  
Chemical System ◽  
Zagreb Indices ◽  
Chemical Structures ◽  
The One ◽  
Atom Bond

We have studied topological indices of the one the hardest crystal structures in a given chemical system, namely, M-carbon. These structures are based and obtained by the famous algorithm USPEX. The computations and applications of topological indices in the study of chemical structures is growing exponentially. Our aim in this article is to compare and compute some well-known topological indices based on degree and sum of degrees, namely, general Randić indices, Zagreb indices, atom bond connectivity index, geometric arithmetic index, new Zagreb indices, fourth atom bond connectivity index, fifth geometric arithmetic index, and Sanskruti index of the M-carbon M r , s , t . Moreover, we have also computed closed formulas for these indices.

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 Extremal topological indices for graphs of given connectivity

Filomat ◽  
2015 ◽  
Vol 29 (7) ◽  
pp. 1639-1643 ◽  
Author(s):  
Ioan Tomescu ◽  
Misbah Arshad ◽  
Muhammad Jamil
Keyword(s):  
Wiener Index ◽  
Topological Indices ◽  
Connectivity Index ◽  
Zeroth Order ◽  
Edge Connectivity ◽  
Connected Graphs ◽  
Randic Index ◽  
Randić Connectivity Index ◽  
Unique Graph ◽  
General Randić Connectivity Index

In this paper, we show that in the class of graphs of order n and given (vertex or edge) connectivity equal to k (or at most equal to k), 1 ? k ? n - 1, the graph Kk + (K1? Kn-k-1) is the unique graph such that zeroth-order general Randic index, general sum-connectivity index and general Randic connectivity index are maximum and general hyper-Wiener index is minimum provided ? > 1. Also, for 2-connected (or 2-edge connected) graphs and ? > 0 the unique graph minimizing these indices is the n-vertex cycle Cn.

A differentor-based adaptive ontology-matching approach

2012 ◽  
Vol 38 (5) ◽  
pp. 459-475 ◽  
Author(s):  
Peigang Xu ◽  
Yadong Wang ◽  
Bo Liu
Keyword(s):  
Semantic Web ◽  
Prior Knowledge ◽  
Similarity Measure ◽  
Web Applications ◽  
Similarity Measures ◽  
Experimental Results ◽  
Ontology Matching ◽  
Semantic Features ◽  
One To One ◽  
The One

Ontology matching, aimed at finding semantically related entities from different ontologies, plays an important role in establishing interoperation among Semantic Web applications. Recently, many similarity measures have been proposed to explore the lexical, structural or semantic features of ontologies. However, a key problem is how to integrate various similarities automatically. In this paper, we define a novel metric termed a “differentor” to assess the probability that a similarity measure can find the one-to-one mappings between two ontologies at the entity level, and use it to integrate different similarity measures. The proposed approach can assign weights automatically to each pair of entities from different ontologies without any prior knowledge, and the aggregation task is accomplished based on these weights. The proposed approach has been tested on OAEI2010 benchmarks for evaluation. The experimental results show that the differentor can reflect the performance of individual similarity measures, and a differentor-based aggregation strategy outperforms other existing aggregation strategies.

scholarly journals Topological indices of bipolar fuzzy incidence graph

2021 ◽  
Vol 19 (1) ◽  
pp. 894-903
Author(s):  
Shu Gong ◽  
Gang Hua
Keyword(s):  
Data Transmission ◽  
Wiener Index ◽  
Topological Indices ◽  
Theoretical Chemistry ◽  
Connectivity Index ◽  
Incidence Graph ◽  
Design Data ◽  
Fuzzy Membership Functions ◽  
Wide Range ◽  
Definition Of

Abstract The topological index of graph has a wide range of applications in theoretical chemistry, network design, data transmission, etc. In fuzzy graph settings, these topological indices have completely different definitions and connotations. In this work, we define new Wiener index and connectivity index for bipolar fuzzy incidence graphs, and obtain the characteristics of these indices by means of the definition of fuzzy membership functions. Furthermore, the interrelationship between Wiener index and connectivity index is considered.

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.

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