Augmented Eccentric Connectivity Index of Some Thorn Graphs

The thorn graph GT of a given graph G is obtained by attaching t(>0) pendent vertices to each vertex of G. The pendent edges, called thorns of GT, can be treated as P2 or K2, so that a thorn graph is generalized by replacing P2 by Pm and K2 by Kp and the respective generalizations are denoted by GPm and GKp. The modified eccentric connectivity index of a graph is defined as the sum of the products of eccentricity with the total degree of neighboring vertices, over all vertices of the graph in a hydrogen suppressed molecular structure. In this paper, we give the modified eccentric connectivity index and the concerned polynomial for the thorn graph GT and the generalized thorn graphs GKp and GPm.

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On the Eccentric Connectivity Index of Generalized Thorn Graphs

National Academy Science Letters ◽

10.1007/s40009-014-0311-y ◽

2014 ◽

Vol 38 (2) ◽

pp. 165-168 ◽

Cited By ~ 4

Author(s):

Y. B. Venkatakrishnan ◽

S. Balachandran ◽

K. Kannan

Keyword(s):

Connectivity Index ◽

Eccentric Connectivity Index ◽

Thorn Graphs

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ON ZAGREB INDICES AND ECCENTRIC CONNECTIVITY INDEX OF CERTAIN THORN GRAPHS

International Journal of Pure and Apllied Mathematics ◽

10.12732/ijpam.v106i3.16 ◽

2016 ◽

Vol 106 (3) ◽

Author(s):

U. Mary ◽

A.K. Therese ◽

M.J. Seles ◽

R. Jayasree ◽

J. Kok

Keyword(s):

Connectivity Index ◽

Eccentric Connectivity Index ◽

Zagreb Indices ◽

Thorn Graphs

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On eccentricity-based topological descriptors of water-soluble dendrimers

Zeitschrift für Naturforschung C ◽

10.1515/znc-2018-0123 ◽

2018 ◽

Vol 74 (1-2) ◽

pp. 25-33 ◽

Cited By ~ 11

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.

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