Connective eccentricity index: a novel topological descriptor for predicting biological activity

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

show abstract

“…Gupta and his co-authors [12] introduced the augmented eccentric-connectivity index of a graph, G, and it is defined as…”

Section: Definitions and Notationsmentioning

confidence: 99%

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

et al. 2018

View full text Add to dashboard Cite

show abstract

“…In 2000, Gupta, Singh and Madan [3] introduced another distance-cum-degree based topological descriptor termed the connective eccentricity index:…”

Section: Introductionmentioning

confidence: 99%

First and Second Zagreb Eccentricity Indices of Thorny Graphs

et al. 2017

View full text Add to dashboard Cite

Abstract:The Zagreb eccentricity indices are the eccentricity reformulation of the Zagreb indices. Let H be a simple graph. The first Zagreb eccentricity index (E 1 (H)) is defined to be the summation of squares of the eccentricity of vertices, i.e., E 1 (H) = ∑ u∈V(H) . We obtain the thorny graph of a graph by attaching thorns i.e., vertices of degree one to every vertex of . In this paper, we will find closed formulation for the first Zagreb eccentricity index and second Zagreb eccentricity index of different well known classes of thorny graphs.

show abstract

“…Among these topological indices, as they are called in the area, there is a large family of ones based on the distance, including eccentricity and general distance, in a graph. In 2000, Gupta et al [12] introduced a novel, adjacency-cum-path length based, topological descriptor named as connective eccentricity index (CEI) when investigating the antihypertensive activity of derivatives of N-benzylimidazole. They showed that the results obtained using the connective eccentricity index were better than the corresponding values obtained using Balaban's mean square distance index [4,5] and the accuracy of prediction was found to be about 80 percents in the active range [12].…”

Section: Introductionmentioning

confidence: 99%

“…In 2000, Gupta et al [12] introduced a novel, adjacency-cum-path length based, topological descriptor named as connective eccentricity index (CEI) when investigating the antihypertensive activity of derivatives of N-benzylimidazole. They showed that the results obtained using the connective eccentricity index were better than the corresponding values obtained using Balaban's mean square distance index [4,5] and the accuracy of prediction was found to be about 80 percents in the active range [12]. Moreover, Sharma et al [24] introduced the eccentric connectivity index, for a graph, which has been employed successfully for the development of numerous mathematical models for the prediction of biological activities of diverse nature [13,24,25].…”

Section: Introductionmentioning

confidence: 99%

Some extremal results on the connective eccentricity index of graphs

Das

Liu

2016

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

Please cite this article in press as: K. Xu et al., Some extremal results on the connective eccentricity index of graphs, J. Math. Anal. Appl. (2015), http://dx. AbstractThe connective eccentricity index (CEI) of a graph G is defined asare the eccentricity and the degree of vertex v i , respectively, in G. In this paper we obtain some lower and upper bounds on the connective eccentricity index for all trees of order n and with matching number β and characterize the corresponding extremal trees. And the maximal graphs of order n and with matching number β and n edges have been determined which maximize the connective eccentricity index. Also the extremal graphs with maximal connective eccentricity index are completely characterized among all connected graphs of order n and with matching number β. Moreover we establish some relations between connective eccentricity index and eccentric connectivity index, as another eccentricity-based invariant, of graphs. AMS classification (2010): 05C07, 05C12, 05C35

show abstract

Connective eccentricity index: a novel topological descriptor for predicting biological activity

Cited by 107 publications

References 14 publications

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

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

First and Second Zagreb Eccentricity Indices of Thorny Graphs

Some extremal results on the connective eccentricity index of graphs

Contact Info

Product

Resources

About