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 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 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 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 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 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 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.

Four New/Old Vertex-Degree-Based Topological Indices of HAC5C7[p, q] and HAC5C6C7[p, q] Nanotubes

2017 ◽  
Vol 14 (1) ◽  
pp. 796-799 ◽  
Author(s):  
Yingfang Li ◽  
Li Yan ◽  
Muhammad Kamran Jamil ◽  
Mohammad Reza Farahani ◽  
Wei Gao ◽  
...  
Keyword(s):  
Topological Indices ◽  
Vertex Degree ◽  
Randić Index ◽  
Zagreb Index ◽  
Randic Index ◽  
Second Zagreb Index ◽  
Forgotten Index ◽  
Mathematical Literature

Recently, Gutman et al. presented some vertex-degree based topological indices, that earlier have been considered in the chemical and/or mathematical literature, but, evaded the attention of most mathematical chemists. These are the reciprocal Randic index (RR), the reduced reciprocal Randic index (RRR), the reduced second Zagreb index (RM2) and the forgotten index (F). In this paper, we compute these topological indices of HAC5C7[p, q] and HAC5C6C7[p, q] nanotubes.

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 On Some New Neighborhood Degree-Based Indices for Some Oxide and Silicate Networks

J ◽  
2019 ◽  
Vol 2 (3) ◽  
pp. 384-409
Author(s):  
Sourav Mondal ◽  
Nilanjan De ◽  
Anita Pal
Keyword(s):  
Molecular Structure ◽  
Network Theory ◽  
Topological Index ◽  
Applied Mathematics ◽  
Reaction Network ◽  
Topological Indices ◽  
Zagreb Index ◽  
Second Zagreb Index ◽  
Real World Problems ◽  
Chemical Reaction Network Theory

Topological indices are numeric quantities that describes the topology of molecular structure in mathematical chemistry. An important area of applied mathematics is the chemical reaction network theory. Real-world problems can be modeled using this theory. Due to its worldwide applications, chemical networks have attracted researchers since their foundation. In this report, some silicate and oxide networks are studied, and exact expressions of some newly-developed neighborhood degree-based topological indices named as the neighborhood Zagreb index ( M N ), the neighborhood version of the forgotten topological index ( F N ), the modified neighborhood version of the forgotten topological index ( F N ∗ ), the neighborhood version of the second Zagreb index ( M 2 ∗ ), and neighborhood version of the hyper Zagreb index ( H M N ) are obtained for the aforementioned networks. In addition, a comparison among all the indices is shown graphically.

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