scholarly journals On Eccentric Connectivity Index and Polynomial of Thorn Graph

2012 ◽  
Vol 03 (08) ◽  
pp. 931-934 ◽  
Author(s):  
Nilanjan De
Keyword(s):  
Connectivity Index ◽  
Eccentric Connectivity Index ◽  
Thorn Graph

scholarly journals Modified Eccentric Connectivity of Generalized Thorn Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Nilanjan De ◽  
Anita Pal ◽  
Sk. Md. Abu Nayeem
Keyword(s):  
Molecular Structure ◽  
Connectivity Index ◽  
Total Degree ◽  
Eccentric Connectivity Index ◽  
Pendent Vertices ◽  
Thorn Graphs ◽  
Thorn Graph

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.

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 A lower bound on the eccentric connectivity index of a graph

2012 ◽  
Vol 160 (3) ◽  
pp. 248-258 ◽  
Author(s):  
M.J. Morgan ◽  
S. Mukwembi ◽  
H.C. Swart
Keyword(s):  
Lower Bound ◽  
Connectivity Index ◽  
Eccentric Connectivity Index
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