scholarly journals Connectivity and Wiener Index of Fuzzy Incidence Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-7 ◽  
Author(s):  
Juanyan Fang ◽  
Irfan Nazeer ◽  
Tabasam Rashid ◽  
Jia-Bao Liu
Keyword(s):  
Wiener Index ◽  
Connectivity Index ◽  
Average Connectivity

Connectivity is a key theory in fuzzy incidence graphs FIGs . In this paper, we introduced connectivity index CI , average connectivity index ACI , and Wiener index WI of FIGs . Three types of nodes including fuzzy incidence connectivity enhancing node FICEN , fuzzy incidence connectivity reducing node FICRN , and fuzzy incidence connectivity neutral node FICNN are also discussed in this paper. A correspondence between WI and CI of a FIG is also computed.

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 QSAR and QSPR study of derivatives 4-arylaminocoumarin

2003 ◽  
Vol 3 (3) ◽  
pp. 59-63
Author(s):  
Davorka Završnik ◽  
Samija Muratović ◽  
Selma Špirtović
Keyword(s):  
Inhibition Zone ◽  
Wiener Index ◽  
Quantitative Structure Activity Relationship ◽  
Connectivity Index ◽  
Activity Relationship ◽  
Log P ◽  
Structure Activity ◽  
Hiv Virus ◽  
Coumarin Compounds ◽  
Structure Properties

Coumarin and its derivatives are reactive compounds, suitable for many syntheses. They are used as anticoagulants, antibacterial, animistic compounds. The interest in coumarins has increased because it was found that they reduce the HIV virus activity. The synthesis of 4-arylaminocoumarin derivatives from 4-hydroxycoumarin, has been carried out, and their antimycotic effects were tested. In the QSAR (quantitative structure-activity relationship) QSPR (quantitativestructure-property-activity relationship) study we have used physicochemical properties and topological indices (Balaban index J(G), Wiener index W(G), information-theoretical index I(G), and valence connectivity index (G), to predict bioactivity of the newly synthesized coumarin compounds. By using methods of molecular modelling, the relationships between structure, properties and activity of coumarin compounds have been investigated. The best QSPR models were obtained using valence connectivity index or combination indices. According Rekker's method the best correlation of calculated values log P, has been obtained with the model based on the inhibition zone (I) 4-arylaminocoumarin derivatives expressed in mm. The results obtained in this study enable further synthesis of new coumarin derivatives and predict their biological activity and properties.

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.

The extended hyper-Wiener index

2003 ◽  
Vol 81 (9) ◽  
pp. 992-996 ◽  
Author(s):  
X H Li
Keyword(s):  
Predictive Ability ◽  
Wiener Index ◽  
Connectivity Index ◽  
Molecular Connectivity ◽  
Molecular Connectivity Index ◽  
Straight Line ◽  
Wiener Number ◽  
Good Potential ◽  
Definition Of ◽  
Leave One Out

According to the definition of molecular connectivity and the definition of a hyper-Wiener index, a novel set of hyper-Wiener indexes (Rn, mRn) are defined and are named the extended hyper-Wiener indexes. Where n = 1, 2, 3, 4,... represents the type of subgraph units and is the number of endmost atoms of the subgraph unit, m is the number of atoms of the subgraph unit. Here n = 1 means the subgraph unit is an atom, n = 2 means the subgraph units are straight-line combinations of m atoms (m = 2, 3, 4, 5, 6,...), and n = 3 means the subgraph units are Y types of combinations of m atoms (m = 4, 5, 6, 7, 8,...), and so on. The potential usefulness of the extended hyper-Wiener index in QSAR and (or) QSPR is evaluated by its correlation with a number of C3–C8 alkanes and by a favorable comparison with models based on the molecular connectivity index and the overall Wiener index. To verify the robustness and the predictive ability of the models, a cross-validation procedure, leave-one-out, and a random test were also performed. The results show that the extended hyper-Wiener indexes examined demonstrate a good potential for QSAR and QSPR studies. Considerably better statistics are obtained when extending the hyper-Wiener index to the extended hyper-Wiener index. The extended hyper-Wiener indexes provided statistical results as good as the molecular connectivity indexes and the overall Wiener index in all models, and the standard deviations provided by these three sets of indexes are rather close. Moreover, this method may provide a better way to apply the Wiener number and the hyper-Wiener index to the system of unsaturated hydrocarbons and organic compounds, including heteroatoms, according to the method of the molecular connectivity index. This can extend the usefulness of the Wiener number and hyper-Wiener index and can make them a kind of widely used topological index in practice.Key words: hyper-Wiener index (R), extended hyper-Wiener index, molecular connectivity index.

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.

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.

Further results on Zagreb eccentricity coindices

2020 ◽  
Vol 12 (06) ◽  
pp. 2050075
Author(s):  
Mahdieh Azari
Keyword(s):  
Wiener Index ◽  
Connectivity Index ◽  
Lower And Upper Bounds ◽  
Graph Invariants ◽  
Eccentric Connectivity Index ◽  
Size Number ◽  
Connectivity Indices ◽  
Degree Distance ◽  
Graph Parameters ◽  
Eccentric Distance

The eccentric connectivity index and second Zagreb eccentricity index are well-known graph invariants defined as the sums of contributions dependent on the eccentricities of adjacent vertices over all edges of a connected graph. The coindices of these invariants have recently been proposed by considering analogous contributions from the pairs of non-adjacent vertices. Here, we obtain several lower and upper bounds on the eccentric connectivity coindex and second Zagreb eccentricity coindex in terms of some graph parameters such as order, size, number of non-adjacent vertex pairs, radius, and diameter, and relate these invariants to some well-known graph invariants such as Zagreb indices and coindices, status connectivity indices and coindices, ordinary and multiplicative Zagreb eccentricity indices, Wiener index, degree distance, total eccentricity, eccentric connectivity index, second eccentric connectivity index, and eccentric-distance sum. Moreover, we compute the values of these coindices for two graph constructions, namely, double graphs and extended double graphs.

TOPOLOGICAL MODELS FOR THE PREDICTION OF NEUTRAL ENDOPEPTIDASE AND ANGIOTENSIN-CONVERTING ENZYME INHIBITORY ACTIVITY OF MERCAPTOACYLDIPEPTIDES

2006 ◽  
Vol 05 (03) ◽  
pp. 565-577 ◽  
Author(s):  
VINEY LATHER ◽  
A. K. MADAN
Keyword(s):  
Inhibitory Activity ◽  
Topological Index ◽  
Wiener Index ◽  
Neutral Endopeptidase ◽  
Connectivity Index ◽  
Molecular Connectivity ◽  
Ace Inhibitory Activity ◽  
Eccentric Connectivity Index ◽  
Data Set ◽  
Molecular Connectivity Index

The relationship between the topological indices and the Neutral Endopeptidase (NEP) inhibitory activity and Angiotensin-Converting Enzyme (ACE) inhibitory activity of mercaptoacyldipeptides has been investigated. Three topological indices — the Wiener index (a distance-based topological index), the molecular connectivity index (an adjacency-based topological index), and the eccentric connectivity index (an adjacency-cum-distance-based topological index), were presently used for investigation. A data set comprising 39 differently substituted mercaptoacyldipeptides was selected for the present study. The values of the Wiener index, molecular connectivity index, and eccentric connectivity index for each of the 39 compounds comprising the data set were computed using an in-house computer program. Resultant data were analyzed and suitable models were developed after identification of the active ranges. Subsequently, a biological activity was assigned to each compound using these models, and the biological activity was then compared with the reported NEP and ACE inhibitory activity of each compound. Accuracy of prediction up to a maximum of ~91% was obtained using these models.

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