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.

scholarly journals The Extremal Graphs of Some Topological Indices with Given Vertex k-Partiteness

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 271 ◽  
Author(s):  
Fang Gao ◽  
Xiaoxin Li ◽  
Kai Zhou ◽  
Jia-Bao Liu
Keyword(s):  
Wiener Index ◽  
Topological Indices ◽  
Extremal Graphs ◽  
Zeroth Order ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Randic Index ◽  
Laplacian Energy ◽  
Modified Wiener Index ◽  
Extremal Value

The vertex k-partiteness of graph G is defined as the fewest number of vertices whose deletion from G yields a k-partite graph. In this paper, we characterize the extremal value of the reformulated first Zagreb index, the multiplicative-sum Zagreb index, the general Laplacian-energy-like invariant, the general zeroth-order Randić index, and the modified-Wiener index among graphs of order n with vertex k-partiteness not more than m .

Topological aspects of some dendrimer structures

2018 ◽  
Vol 7 (2) ◽  
pp. 123-129 ◽  
Author(s):  
Adnan Aslam ◽  
Muhammad Kamran Jamil ◽  
Wei Gao ◽  
Waqas Nazeer
Keyword(s):  
Self Assembly ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Topological Indices ◽  
Connectivity Index ◽  
Molecular Topology ◽  
Zinc Porphyrin ◽  
Physico Chemical ◽  
Randić Connectivity Index ◽  
Atom Bond

AbstractA numerical number associated to the molecular graphGthat describes its molecular topology is called topological index. In the study ofQSARandQSPR, topological indices such as atom-bond connectivity index, Randić connectivity index, geometric index, etc. help to predict many physico-chemical properties of the chemical compound under study. Dendrimers are macromolecules and have many applications in chemistry, especially in self-assembly procedures and host-guest reactions. The aim of this report is to compute degree-based topological indices, namely the fourth atom-bond connectivity index and fifth geometric arithmetic index of poly propyl ether imine, zinc porphyrin, and porphyrin dendrimers.

scholarly journals Computation of Topological Indices of Graphene

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
G. Sridhara ◽  
M. R. Rajesh Kanna ◽  
R. S. Indumathi
Keyword(s):  
Topological Indices ◽  
Connectivity Index ◽  
Randić Connectivity Index ◽  
Abc Index ◽  
Ga Index

We compute ABC index, ABC4index, Randic connectivity index, Sum connectivity index, GA index, and GA5index of Graphene.

scholarly journals Comparing the molecular graph degeneracy of Wiener, Harary, Balaban, Randi´c and ZEP topological indices

2014 ◽  
Vol 23 (2) ◽  
pp. 165-174
Author(s):  
ZOITA-MARIOARA BERINDE ◽  
Keyword(s):  
Topological Index ◽  
Molecular Graph ◽  
Wiener Index ◽  
Topological Indices ◽  
Randić Index ◽  
Discrimination Power ◽  
Harary Index ◽  
Molecular Chemistry ◽  
Randic Index

The aim of this paper is to show that the ZEP topological index has better discrimination power than four well known topological indices in molecular chemistry: Balaban index, Harary index, Randic index, and Wiener index.

scholarly journals Study of Hardness of Superhard Crystals by Topological Indices

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Xiujun Zhang ◽  
Muhammad Naeem ◽  
Abdul Qudair Baig ◽  
Manzoor Ahmad Zahid
Keyword(s):  
Molecular Structure ◽  
Chemical Structure ◽  
Topological Indices ◽  
Connectivity Index ◽  
Chemical Bonds ◽  
Randić Index ◽  
Total Resistance ◽  
Randic Index ◽  
Atom Bond

Topological indices give immense information about a molecular structure or chemical structure. The hardness of materials for the indentation can be defined microscopically as the total resistance and effect of chemical bonds in the respective materials. The aim of this paper is to study the hardness of some superhard B C x crystals by means of topological indices, specifically Randić index and atom-bond connectivity index.

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