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 On Leap Reduced Reciprocal Randic and Leap Reduced Second Zagreb Indices of Some Graphs

2019 ◽  
Vol 3 (2) ◽  
pp. 27-35
Author(s):  
Fazal Dayan ◽  
Muhammad Javaid ◽  
Muhammad Aziz ur Rehman
Keyword(s):  
Topological Indices ◽  
Randić Index ◽  
Zagreb Index ◽  
Randic Index ◽  
Zagreb Indices ◽  
Second Zagreb Index ◽  
Second Degree

Naji et al. introduced the leap Zagreb indices of a graph in 2017 which are new distance-degree-based topological indices conceived depending on the second degree of vertices. In this paper, we have defined the first and second leap reduced reciprocal Randic index and leap reduced second Zagreb index for selected wheel related graphs.

scholarly journals Topological Indices of Dendrimers used in Drug Delivery

2020 ◽  
Vol 12 (4) ◽  
pp. 645-655
Author(s):  
T. P. Jude ◽  
E. Panchadcharam ◽  
K. Masilamani
Keyword(s):  
Drug Delivery ◽  
Molecular Graph ◽  
Topological Indices ◽  
Vertex Degree ◽  
Numerical Representation ◽  
Chemical Bonds ◽  
Randić Index ◽  
Zagreb Index ◽  
Randic Index ◽  
Carrier Vehicle

The topological index is a numerical representation of a molecular structure. In chemical graphs, the atoms and the chemical bonds between them are represented by vertices and edges respectively. Vertex degree based topological indices are the most studied and mostly used type of topological indices. The mostly used vertex degree based topological indices in the field of drug design and developments are the Zagreb index and the Randić index. The structural chemistry of dendrimers could be manipulated by their topological indices to get the specific structure with required properties to deliver the drugs to target carrier vehicle. In this work, topological indices of three types of dendrimers which are used as the drug delivery system were studied and their Zagreb index and the Randić index were calculated using molecular graph theory. Moreover, the other versions of these two indices were also calculated to these dendrimers.

scholarly journals On the Number of Spanning Trees of Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Ş. Burcu Bozkurt ◽  
Durmuş Bozkurt
Keyword(s):  
Spanning Trees ◽  
Vertex Degree ◽  
Randić Index ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Connected Graphs ◽  
Randic Index ◽  
Number Of Spanning Trees

We establish some bounds for the number of spanning trees of connected graphs in terms of the number of vertices(n), the number of edges(m), maximum vertex degree(Δ1), minimum vertex degree(δ),…first Zagreb index(M1),and Randić index(R-1).

scholarly journals Several Topological Indices of Two Kinds of Tetrahedral Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Jia-Bao Liu ◽  
Lu-Lu Fang
Keyword(s):  
Finite Element ◽  
Network Model ◽  
Topological Indices ◽  
Randić Index ◽  
Zagreb Index ◽  
Randic Index ◽  
Research Studies

Tetrahedral network is considered as an effective tool to create the finite element network model of simulation, and many research studies have been investigated. The aim of this paper is to calculate several topological indices of the linear and circle tetrahedral networks. Firstly, the resistance distances of the linear tetrahedral network under different classifications have been calculated. Secondly, according to the above results, two kinds of degree-Kirchhoff indices of the linear tetrahedral network have been achieved. Finally, the exact expressions of Kemeny’s constant, Randic index, and Zagreb index of the linear tetrahedral network have been deduced. By using the same method, the topological indices of circle tetrahedral network have also been obtained.

scholarly journals Topology-Based Analysis of OTIS (Swapped) Networks OKn and OPn

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Hai-Xia Li ◽  
Sarfaraz Ahmad ◽  
Iftikhar Ahmad
Keyword(s):  
Topological Index ◽  
Molecular Descriptor ◽  
Randić Index ◽  
Zagreb Index ◽  
Randic Index ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Second Zagreb Index ◽  
Chemical Graph Theory ◽  
Augmented Zagreb Index

In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. In this paper, M-polynomial OKn and OPn networks are computed. The M-polynomial is rich in information about degree-based topological indices. By applying the basic rules of calculus on M-polynomials, the first and second Zagreb indices, modified second Zagreb index, general Randić index, inverse Randić index, symmetric division index, harmonic index, inverse sum index, and augmented Zagreb index are recovered.

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 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 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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