scholarly journals Computing topological indices of the line graphs of Banana tree graph and Firecracker graph

2017 ◽  
Vol 2 (1) ◽  
pp. 83-92 ◽  
Author(s):  
Muhammad Shoaib Sardar ◽  
Sohail Zafar ◽  
Zohaib Zahid
Keyword(s):  
Connectivity Index ◽  
Line Graphs ◽  
Tree Graph ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Second Zagreb Index ◽  
Banana Tree ◽  
Randić Connectivity Index ◽  
Augmented Zagreb Index ◽  
Atom Bond

AbstractIn this paper, we compute first Zagreb index (coindex), second Zagreb index (coindex), third Zagreb index, first hyper-Zagreb index, atom-bond connectivity index, fourth atom-bond connectivity index, sum connectivity index, Randić connectivity index, augmented Zagreb index, Sanskruti index, geometric-arithmetic connectivity index and fifth geometric-arithmetic connectivity index of the line graphs of Banana tree graph and Firecracker graph.

scholarly journals Topological Indices of the Pent-Heptagonal Nanosheets VC5C7 and HC5C7

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Fei Deng ◽  
Xiujun Zhang ◽  
Mehdi Alaeiyan ◽  
Abid Mehboob ◽  
Mohammad Reza Farahani
Keyword(s):  
Topological Indices ◽  
Connectivity Index ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Second Zagreb Index ◽  
Randić Connectivity Index ◽  
Augmented Zagreb Index ◽  
Forgotten Index ◽  
Atom Bond ◽  
Modified Zagreb Index

In this paper, we computed the topological indices of pent-heptagonal nanosheet. Formulas for atom-bond connectivity index, fourth atom-bond connectivity index, Randić connectivity index, sum-connectivity index, first Zagreb index, second Zagreb index, augmented Zagreb index, modified Zagreb index, hyper Zagreb index, geometric-arithmetic index, fifth geometric-arithmetic index, Sanskruti index, forgotten index, and harmonic index of pent-heptagonal nanosheet have been derived.

scholarly journals Eccentricity-Based Topological Indices of a Cyclic Octahedron Structure

Mathematics ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 141 ◽  
Author(s):  
Manzoor Zahid ◽  
Abdul Baig ◽  
Muhammad Naeem ◽  
Muhammad Azhar
Keyword(s):  
Connectivity Index ◽  
First Zagreb Index ◽  
Eccentric Connectivity Index ◽  
Zagreb Index ◽  
Chemical Graph ◽  
Second Zagreb Index ◽  
The Third ◽  
Average Eccentricity ◽  
The First Zagreb Index ◽  
Atom Bond

In this article, we study the chemical graph of a cyclic octahedron structure of dimension n and compute the eccentric connectivity polynomial, the eccentric connectivity index, the total eccentricity, the average eccentricity, the first Zagreb index, the second Zagreb index, the third Zagreb index, the atom bond connectivity index and the geometric arithmetic index of the cyclic octahedron structure. Furthermore, we give the analytically closed formulas of these indices which are helpful for studying the underlying topologies.

scholarly journals On molecular topological properties of benzenoid structures

2016 ◽  
Vol 94 (8) ◽  
pp. 687-698 ◽  
Author(s):  
Shehnaz Akhter ◽  
Muhammad Imran
Keyword(s):  
Strain Energy ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Connectivity Index ◽  
Line Graphs ◽  
Zigzag Edge ◽  
Zagreb Index ◽  
Chemical Significance ◽  
Randić Connectivity Index ◽  
Atom Bond

The degree-based topological indices correlate certain physicochemical properties such as boiling point, strain energy, and stability, etc., of certain chemical compounds. Among the major classes of topological indices are the distance-based topological indices, degree-based topological indices, and counting-related polynomials and corresponding indices of graphs. Among all of the degree-based indices, namely the first general Zagreb index, general Rndić connectivity index, general sum-connectivity index, atom–bond connectivity index (ABC), and geometric–arithmetic index (GA), are most important due to their chemical significance. In this paper, we compute the first general Zagreb index, general Randić connectivity index, general sum-connectivity index, ABC, GA, ABC4, and GA5 indices of hexagonal parallelogram P(m,n) nanotubes, triangular benzenoid Gn, and zigzag-edge coronoid fused with starphene ZCS(k,l,m) nanotubes by using the line graphs of the subdivision of these chemical graphs.

scholarly journals Topological Indices of H-Naphtalenic Nanosheet

2018 ◽  
Vol 16 (1) ◽  
pp. 1184-1188 ◽  
Author(s):  
Nazeran Idrees ◽  
Muhammad Jawwad Saif ◽  
Afshan Sadiq ◽  
Asia Rauf ◽  
Fida Hussain
Keyword(s):  
Chemical Structure ◽  
Topological Indices ◽  
Connectivity Index ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Chemical Graph ◽  
Second Zagreb Index ◽  
Topological Descriptor ◽  
Chemical Graph Theory ◽  
Atom Bond

AbstractIn chemical graph theory, a single numeric number related to a chemical structure is called a topological descriptor or topological index of a graph. In this paper, we compute analytically certain topological indices for H-Naphtalenic nanosheet like Randic index, first Zagreb index, second Zagreb index, geometric arithmetic index, atom bond connectivity index, sum connectivity index and hyper-Zagreb index using edge partition technique. The first multiple Zagreb index and the second multiple Zagreb index of the nanosheet are also discussed in this paper.

scholarly journals Topological Indices of Vitamin D3

2018 ◽  
Vol 7 (4) ◽  
pp. 6276
Author(s):  
Rajesh Kanna ◽  
Roopa S ◽  
PARASHIVAMURTHY H L
Keyword(s):  
Vitamin D3 ◽  
Topological Index ◽  
Topological Indices ◽  
Connectivity Index ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Second Zagreb Index ◽  
Augmented Zagreb Index ◽  
Abc Index ◽  
Ga Index

Graph theory has provided chemists with a variety of useful tools, such as topological indices. A topological index Top(G) of a graph G is a number with the property that for every graph H isomorphic to G, Top(H) = Top(G). In this paper, we compute ABC index, ABC4 index, Randi´c connectivity index, Sum connectivity index, GA index , GA5 index, First Zagreb index, Second Zagreb index, First Multiple Zagreb index, Second Multiple Zagreb index, Augmented Zagreb index, Harmonic index and Hyper Zagreb index, First Zagreb polynomial, Second Zagreb polynomial, Third Zagreb polynomial, Forgotten polynomials, Forgotten topological index and Symmetric division index of vitamin D3.

scholarly journals Topological Indices of Certain Transformed Chemical Structures

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Xuewu Zuo ◽  
Jia-Bao Liu ◽  
Hifza Iqbal ◽  
Kashif Ali ◽  
Syed Tahir Raza Rizvi
Keyword(s):  
Carbon Nanotube ◽  
Line Graph ◽  
Topological Indices ◽  
Connectivity Index ◽  
Zagreb Index ◽  
Harmonic Index ◽  
Chemical Structures ◽  
Augmented Zagreb Index ◽  
Carbon Nanotube Networks ◽  
Atom Bond

Topological indices like generalized Randić index, augmented Zagreb index, geometric arithmetic index, harmonic index, product connectivity index, general sum-connectivity index, and atom-bond connectivity index are employed to calculate the bioactivity of chemicals. In this paper, we define these indices for the line graph of k-subdivided linear [n] Tetracene, fullerene networks, tetracenic nanotori, and carbon nanotube networks.

scholarly journals Vertex-Based Topological Indices of Double and Strong Double Graph of Dutch Windmill Graph

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Muhammad Asad Ali ◽  
Muhammad Shoaib Sardar ◽  
Imran Siddique ◽  
Dalal Alrowaili
Keyword(s):  
Graph Theory ◽  
Chemical Properties ◽  
Topological Indices ◽  
Connectivity Index ◽  
Vaporization Enthalpy ◽  
Zagreb Index ◽  
Graph Operations ◽  
Big Graphs ◽  
Physical And Chemical ◽  
Atom Bond

A measurement of the molecular topology of graphs is known as a topological index, and several physical and chemical properties such as heat formation, boiling point, vaporization, enthalpy, and entropy are used to characterize them. Graph theory is useful in evaluating the relationship between various topological indices of some graphs derived by applying certain graph operations. Graph operations play an important role in many applications of graph theory because many big graphs can be obtained from small graphs. Here, we discuss two graph operations, i.e., double graph and strong double graph. In this article, we will compute the topological indices such as geometric arithmetic index GA , atom bond connectivity index ABC , forgotten index F , inverse sum indeg index ISI , general inverse sum indeg index ISI α , β , first multiplicative-Zagreb index PM 1   and second multiplicative-Zagreb index PM 2 , fifth geometric arithmetic index GA 5 , fourth atom bond connectivity index ABC 4 of double graph, and strong double graph of Dutch Windmill graph D 3 p .

scholarly journals Topological indices of non-commuting graph of dihedral groups

2018 ◽  
Vol 14 ◽  
pp. 473-476 ◽  
Author(s):  
Nur Idayu Alimon ◽  
Nor Haniza Sarmin ◽  
Ahmad Erfanian
Keyword(s):  
Wiener Index ◽  
Topological Indices ◽  
First Zagreb Index ◽  
Dihedral Groups ◽  
Zagreb Index ◽  
Second Zagreb Index ◽  
Commuting Graph ◽  
Vertex Set ◽  
Group A ◽  
Group Of Symmetries

Assume  is a non-abelian group  A dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. The non-commuting graph of  denoted by  is the graph of vertex set  whose vertices are non-central elements, in which  is the center of  and two distinct vertices  and  are joined by an edge if and only if  In this paper, some topological indices of the non-commuting graph,  of the dihedral groups,  are presented. In order to determine the Edge-Wiener index, First Zagreb index and Second Zagreb index of the non-commuting graph,  of the dihedral groups,  previous results of some of the topological indices of non-commuting graph of finite group are used. Then, the non-commuting graphs of dihedral groups of different orders are found. Finally, the generalisation of Edge-Wiener index, First Zagreb index and Second Zagreb index of the non-commuting graphs of dihedral groups are determined.

scholarly journals Hyper Zagreb indices of composite graphs

2016 ◽  
Vol 4 (2) ◽  
pp. 47 ◽  
Author(s):  
Sharmila Devi ◽  
V. Kaladevi
Keyword(s):  
Molecular Graph ◽  
Sum Of Squares ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Second Zagreb Index ◽  
The First Zagreb Index ◽  
Thorn Graph

For a (molecular) graph, the first Zagreb index M1 is equal to the sum of squares of the degrees of vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. Similarly, the hyper Zagreb index is defined as the sum of square of degree of vertices over all the edges.  In this paper, First we obtain the hyper Zagreb indices of some derived graphs and the generalized transformations graphs. Finally, the hyper Zagreb indices of double, extended double, thorn graph, subdivision vertex corona of graphs, Splice and link graphs are obtained.

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.

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