scholarly journals Certain topological indices and polynomials for the semitotal-point graph and line graph of semitotal-point graph for Dutch windmill graph

2020 ◽  
Vol 3 (2) ◽  
pp. 63
Author(s):  
Salma Kanwal ◽  
Mariam Imtiaz ◽  
Ayesha Manzoor ◽  
Nazeeran Idrees ◽  
Ammara Afzal
Keyword(s):  
Line Graph ◽  
Topological Indices ◽  
Point Graph ◽  
Zagreb Index ◽  
Harmonic Index ◽  
Zagreb Indices ◽  
Symmetric Division ◽  
Augmented Zagreb Index ◽  
Forgotten Index

<p>Dutch windmill graph [1, 2] and denoted by <em>Dnm</em>. Order and size of Dutch windmill graph are (<em>n</em>−1)<em>m</em>+1 and mn respectively. In this paper, we computed certain topological indices and polynomials i.e. Zagreb polynomials, hyper Zagreb, Redefined Zagreb indices, modified first Zagreb, Reduced second Zagreb, Reduced Reciprocal Randi´c, 1st Gourava index, 2nd Gourava index, 1st hyper Gourava index, 2nd hyper Gourava index, Product connectivity Gourava index, Sum connectivity Gourava index, Forgotten index, Forgotten polynomials, <em>M</em>-polynomials and some topological indices in term of the <em>M</em>-polynomials i.e. 1st Zagreb index, 2nd Zagreb index, Modified 2nd Zagreb, Randi´c index, Reciprocal Randi´c index, Symmetric division, Harmonic index, Inverse Sum index, Augmented Zagreb index for the semitotal-point graph and line graph of semitotal-point graph for Dutch windmill graph.</p>

scholarly journals On Analysis of Topological Aspects for Subdivision of Kragujevac Tree Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Salma Kanwal ◽  
Shanshan Shang ◽  
Muhammad Kamran Siddiqui ◽  
Tahira Sumbal Shaikh ◽  
Ammara Afzal ◽  
...  
Keyword(s):  
Line Graph ◽  
Topological Indices ◽  
Zagreb Index ◽  
Tree Networks ◽  
Harmonic Index ◽  
Symmetric Division ◽  
Second Zagreb Index ◽  
Augmented Zagreb Index ◽  
Forgotten Index ◽  
Topological Characteristics

In this paper, we have taken review of certain topological topological characteristics of subdivision and the line graph of subdivision of Kragujevac tree. A Kragujevac tree is denoted by K , K ∈ Kg q = r 2 t + 1 + 1 , r , with order r 2 t + 1 + 1 and size r 2 t + 1 , respectively. We have computed the Zagreb polynomials, forgotten polynomial, and M-polynomial for Kragujevac tree. Moreover, we have computed topological indices like Zagreb-type indices, reduced reciprocal Randić indices, family of Gourava indices as well as forgotten index. Further, some topological indices that can be directly derived from M-polynomial, i.e., first and second Zagreb index, modified second Zagreb index, Randić and reciprocal Randić index, symmetric division and harmonic index, and inverse sum and augmented Zagreb index are also computed.

scholarly journals M-Polynomials and Degree-Based Topological Indices of the Molecule Copper(I) Oxide

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Faryal Chaudhry ◽  
Iqra Shoukat ◽  
Deeba Afzal ◽  
Choonkil Park ◽  
Murat Cancan ◽  
...  
Keyword(s):  
Topological Indices ◽  
Randić Index ◽  
Zagreb Index ◽  
Harmonic Index ◽  
Randic Index ◽  
Zagreb Indices ◽  
Symmetric Division ◽  
Augmented Zagreb Index ◽  
Physical And Chemical ◽  
Modified Zagreb Index

Topological indices are numerical parameters used to study the physical and chemical residences of compounds. Degree-based topological indices have been studied extensively and can be correlated with many properties of the understudy compounds. In the factors of degree-based topological indices, M-polynomial played an important role. In this paper, we derived closed formulas for some well-known degree-based topological indices like first and second Zagreb indices, the modified Zagreb index, the symmetric division index, the harmonic index, the Randić index and inverse Randić index, and the augmented Zagreb index using calculus.

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 Some Topological Indices and their Polynomials of Graphene

2019 ◽  
Vol 35 (5) ◽  
pp. 1514-1518 ◽  
Author(s):  
H.L. Parashivamurthy ◽  
M.R.Rajesh Kanna ◽  
R. Jagadeesh
Keyword(s):  
Topological Indices ◽  
Zagreb Index ◽  
Symmetric Division ◽  
Division Polynomial ◽  
Forgotten Index

In this manuscript we have computed third Zagreb index, first Zagreb polynomial, second Zagreb polynomial, third Zagreb polynomial, hyper Zagreb polynomial, forgotten index, forgotten polynomial, symmetric division index and symmetric division polynomial of Graphene. These quantities are based on degrees of the vertices.

scholarly journals Computing Topological Indices and Polynomials for Line Graphs

Mathematics ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 137 ◽  
Author(s):  
Shahid Imran ◽  
Muhammad Siddiqui ◽  
Muhammad Imran ◽  
Muhammad Nadeem
Keyword(s):  
Topological Index ◽  
Line Graph ◽  
Topological Indices ◽  
Line Graphs ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Second Zagreb Index ◽  
Vertex Degrees ◽  
Set Up ◽  
Ladder Graphs

A topological index is a number related to the atomic index that allows quantitative structure–action/property/toxicity connections. All the more vital topological indices correspond to certain physico-concoction properties like breaking point, solidness, strain vitality, and so forth, of synthetic mixes. The idea of the hyper Zagreb index, multiple Zagreb indices and Zagreb polynomials was set up in the substance diagram hypothesis in light of vertex degrees. These indices are valuable in the investigation of calming exercises of certain compound systems. In this paper, we computed the first and second Zagreb index, the hyper Zagreb index, multiple Zagreb indices and Zagreb polynomials of the line graph of wheel and ladder graphs by utilizing the idea of subdivision.

scholarly journals Some Algebraic Polynomials and Topological Indices of Octagonal Network

2016 ◽  
Author(s):  
Young Chel Kwun ◽  
Waqas Nazeer ◽  
Mobeen Munir ◽  
Shin Min Kang
Keyword(s):  
Graphical Representation ◽  
Topological Indices ◽  
Molecular Structures ◽  
Quantitative Structure ◽  
Structure Property ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Structure Activity ◽  
Activity Structure ◽  
Augmented Zagreb Index

M-polynomial of different molecular structures helps to calculate many topological indices. A topological index of graph G is a numerical parameter related to G which characterizes its molecular topology and is usually graph invariant. In the field of quantitative structure-activity (QSAR) quantitative structure-activity structure-property (QSPR) research, theoretical properties of the chemical compounds and their molecular topological indices such as the Zagreb indices, Randic index, Symmetric division index, Harmonic index, Inverse sum index, Augmented Zagreb index, multiple Zagreb indices etc. are correlated. In this report, we compute closed forms of M-polynomial, first Zagreb polynomial and second Zagreb polynomial of Octagonal network. From the M-polynomial we recover some degree-based topological indices for Octagonal network. Moreover, we give a graphical representation of our results.

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 Computational Analysis of new Degree-based descriptors of oxide networks

2019 ◽  
Vol 17 (1) ◽  
pp. 177-182 ◽  
Author(s):  
Zafar Hussain ◽  
Mobeen Munir ◽  
Muhammad Bilal ◽  
Alam Ameer ◽  
Shazia Rafique ◽  
...  
Keyword(s):  
Computational Analysis ◽  
Graphical Analysis ◽  
Topological Indices ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Molecular Graphs ◽  
Pharmaceutical Industries ◽  
Forgotten Index

AbstractOxide networks have diverse applications in the polymer and pharmaceutical industries. Polynomials and degree-based topological indices have tendencies to correlate properties of molecular graphs. In this article, we formulate the closed forms of Zagreb and forgotten polynomials and topological indices such as Hyper-Zagreb index, first and second multiple Zagreb indices, forgotten index, Albert index, Bell index, IRM(G) of oxide networks. We also compute the F-index of complement of oxide networks, F-coindex of G and F-coindex of complement of oxide networks. We put graphical analysis of each index with respect to the parameter involved in each case.

scholarly journals Topological properties of Graphene using some novel neighborhood degree-based topological indices

2019 ◽  
Vol 11 (01) ◽  
pp. 1950006 ◽  
Author(s):  
Sourav Mondal ◽  
Nilanjan De ◽  
Anita Pal
Keyword(s):  
Real Number ◽  
Chemical Structure ◽  
Topological Index ◽  
Line Graph ◽  
Topological Indices ◽  
Index Formula ◽  
Topological Properties ◽  
Zagreb Index ◽  
Physiochemical Properties ◽  
Second Zagreb Index

Topological indices are numeric quantities that transform chemical structure to real number. Topological indices are used in QSAR/QSPR studies to correlate the bioactivity and physiochemical properties of molecule. In this paper, some newly designed neighborhood degree-based topological indices named as neighborhood Zagreb index ([Formula: see text]), neighborhood version of Forgotten topological index ([Formula: see text]), modified neighborhood version of Forgotten topological index ([Formula: see text]), neighborhood version of second Zagreb index ([Formula: see text]) and neighborhood version of hyper Zagreb index ([Formula: see text]) are obtained for Graphene and line graph of Graphene using subdivision idea. In addition, these indices are compared graphically with respect to their response for Graphene and line graph of subdivision of Graphene.

scholarly journals Valency-based molecular descriptors of Bakelite network BNmn$B\text N_{m}^{n}$

2019 ◽  
Vol 17 (1) ◽  
pp. 663-670 ◽  
Author(s):  
Maqsood Ahmad ◽  
Muhammad Javaid ◽  
Muhammad Saeed ◽  
Chahn Yong Jung
Keyword(s):  
Physical Properties ◽  
Molecular Descriptors ◽  
Molecular Graph ◽  
Synthetic Polymer ◽  
Topological Indices ◽  
Qsar Studies ◽  
Zagreb Indices ◽  
Symmetric Division ◽  
Atom Bond

AbstractBakelite network $BN_{m}^{n}$is a molecular graph of bakelite, a pioneering and revolutionary synthetic polymer (Thermosetting Plastic) and regarded as the material of a thousand uses. In this paper, we aim to compute various degree-based topological indices of a molecular graph of bakelite network $BN_{m}^{n}$. These molecular descriptors play a fundamental role in QSPR/QSAR studies in describing the chemical and physical properties of Bakelite network $BN_{m}^{n}$. We computed atom-bond connectivity ABC its fourth version ABC4 geometric arithmetic GA its fifth version GA5 Narumi-Katayama, sum-connectivity and Sanskruti indices, first, second, modified and augmented Zagreb indices, inverse and general Randic’ indices, symmetric division, harmonic and inverse sum indices of $BN_{m}^{n}$.

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