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

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.

Sharp lower bounds on the sum-connectivity index of quasi-tree graphs

2021 ◽  
pp. 2150136
Author(s):  
Amir Taghi Karimi
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Connectivity Index ◽  
Tree Graphs ◽  
Sharp Lower Bound

The sum-connectivity index of a graph [Formula: see text] is defined as the sum of weights [Formula: see text] over all edges [Formula: see text] of [Formula: see text], where [Formula: see text] and [Formula: see text] are the degrees of the vertices [Formula: see text] and [Formula: see text] in [Formula: see text], respectively. A graph [Formula: see text] is called quasi-tree, if there exists [Formula: see text] such that [Formula: see text] is a tree. In the paper, we give a sharp lower bound on the sum-connectivity index of quasi-tree graphs.

Two-tree graphs with minimum sum-connectivity index

2020 ◽  
pp. 2150053
Author(s):  
A. Jahanbani
Keyword(s):  
Lower Bound ◽  
Complete Graph ◽  
Connectivity Index ◽  
Tree Graphs ◽  
Sharp Lower Bound

The sum-connectivity index of a graph [Formula: see text] is defined as the sum of weights [Formula: see text] over all edges [Formula: see text] of [Formula: see text], where [Formula: see text] and [Formula: see text] are the degrees of the vertices [Formula: see text] and [Formula: see text] in [Formula: see text], respectively. The graphs called two-trees are defined by recursion. The smallest two-tree is the complete graph on two vertices. A two-tree on [Formula: see text] vertices (where [Formula: see text]) is obtained by adding a new vertex adjacent to the two end vertices of one edge in a two-tree on [Formula: see text] vertices. In this paper, the sharp lower bound on the sum-connectivity index of two-trees is presented, and the two-trees with the minimum and the second minimum sum-connectivity, respectively, are determined.

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