Topological indices of non-commuting graph of dihedral groups

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.

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The Wiener and Zagreb Indices of Conjugacy Class Graph of the Dihedral Groups

MATEMATIKA ◽

10.11113/matematika.v35.n1.1102 ◽

2019 ◽

Vol 35 (1) ◽

pp. 51-57 ◽

Cited By ~ 1

Author(s):

Nur Idayu Alimon ◽

Nor Haniza Sarmin ◽

Ahmad Erfanian

Keyword(s):

Conjugacy Class ◽

Chemical Properties ◽

Wiener Index ◽

Topological Indices ◽

Dihedral Groups ◽

Zagreb Index ◽

Vertex Set ◽

Class Graph ◽

The First Zagreb Index ◽

Group Of Symmetries

Topological indices are numerical values that can be analysed to predict the chemical properties of the molecular structure and the topological indices are computed for a graph related to groups. Meanwhile, the conjugacy class graph of is defined as a graph with a vertex set represented by the non-central conjugacy classes of . Two distinct vertices are connected if they have a common prime divisor. The main objective of this article is to find various topological indices including the Wiener index, the first Zagreb index and the second Zagreb index for the conjugacy class graph of dihedral groups of order where the dihedral group is the group of symmetries of regular polygon, which includes rotations and reflections. Many topological indices have been determined for simple and connected graphs in general but not graphs related to groups. In this article, the Wiener index and Zagreb index of conjugacy class graph of dihedral groups are generalized.

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The Topological Indices of the Non-commuting Graph for Symmetric Groups

ASM Science Journal ◽

10.32802/asmscj.2020.sm26(1.28) ◽

2020 ◽

pp. 1-5

Author(s):

Nur Idayu Alimon ◽

Nor Haniza Sarmin ◽

Ahmad Erfanian

Keyword(s):

Symmetric Group ◽

Chemical Compound ◽

Molecular Graph ◽

Symmetric Groups ◽

Wiener Index ◽

Topological Indices ◽

Zagreb Index ◽

Commuting Graph ◽

Central Elements ◽

Vertex Set

Topological indices are the numerical values that can be calculated from a graph and it is calculated based on the molecular graph of a chemical compound. It is often used in chemistry to analyse the physical properties of the molecule which can be represented as a graph with a set of vertices and edges. Meanwhile, the non-commuting graph is the graph of vertex set whose vertices are non-central elements and two distinct vertices are joined by an edge if they do not commute. The symmetric group, denoted as S_n, is a set of all permutation under composition. In this paper, two of the topological indices, namely the Wiener index and the Zagreb index of the non-commuting graph for symmetric groups of order 6 and 24 are determined. Keywords: Wiener index; Zagreb index; non-commuting graph; symmetric groups

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

Mathematics ◽

10.3390/math6110271 ◽

2018 ◽

Vol 6 (11) ◽

pp. 271 ◽

Cited By ~ 1

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 .

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First and Second Zagreb Polynomials of VC5C7[p,q] and HC5C7[p,q]Nanotubes

International Letters of Chemistry Physics and Astronomy ◽

10.18052/www.scipress.com/ilcpa.31.56 ◽

2014 ◽

Vol 31 ◽

pp. 56-62 ◽

Cited By ~ 3

Author(s):

Mohammad Reza Farahani

Keyword(s):

Graph Theory ◽

Connected Graph ◽

Topological Indices ◽

First Zagreb Index ◽

Zagreb Index ◽

Zagreb Indices ◽

Second Zagreb Index ◽

Connectivity Indices ◽

Anti Inflammatory ◽

Simple Connected Graph

Let G = (V,E) be a simple connected graph. The sets of vertices and edges of G are denoted by V = V(G) and E = E(G), respectively. There exist many topological indices and connectivity indices in graph theory. The First and Second Zagreb indices were first introduced by Gutman and Trinajstić In1972. It is reported that these indices are useful in the study of anti-inflammatory activities of certain chemical instances, and in elsewhere. In this paper, we focus on the structure of ”G = VC5C7[p,q]”and ”H = HC5C7[p,q]” nanotubes and counting first Zagreb index Zg1(G) = ∑veVdv2 and Second Zagreb index Zg2(G) =∑e=uveE(G)(du·dv) of G and H, as well as First Zagreb polynomial Zg1(G,x ) =∑e=uveE(G)xdu+dv and Second Zagreb Polynomial Zg2(G,x) = ∑e=uveE(G)xdu·dv

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Topological Indices of H-Naphtalenic Nanosheet

Open Chemistry ◽

10.1515/chem-2018-0131 ◽

2018 ◽

Vol 16 (1) ◽

pp. 1184-1188 ◽

Cited By ~ 2

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.

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Topological Indices of the Pent-Heptagonal Nanosheets VC5C7 and HC5C7

Advances in Materials Science and Engineering ◽

10.1155/2019/9594549 ◽

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.

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Topological Indices of Vitamin D3

International Journal of Engineering & Technology ◽

10.14419/ijet.v7i4.24064 ◽

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.

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Zagreb Connection Indices of Some Nanostructures

Acta Chemica Iasi ◽

10.2478/achi-2018-0011 ◽

2018 ◽

Vol 26 (2) ◽

pp. 169-180 ◽

Cited By ~ 2

Author(s):

Saba Manzoor ◽

Nisar Fatima ◽

Akhlaq Ahmad Bhatti ◽

Akbar Ali

Keyword(s):

Electron Energy ◽

Approximate Formula ◽

Topological Indices ◽

First Zagreb Index ◽

Zagreb Index ◽

Zagreb Indices ◽

Second Zagreb Index ◽

The First Zagreb Index ◽

Molecular Branching

Abstract The first Zagreb index (occurred in an approximate formula of total π-electron energy, communicated in 1972) and the second Zagreb index (appeared in 1975, within the study of molecular branching) are among the most studied topological indices. Recently, three modified versions of the Zagreb indices were proposed independently in [A. Ali, N. Trinajstić, A novel/old modification of the first Zagreb index, arXiv:1705.10430 [math.CO], 2017] and [A. M. Naji, N. D. Soner, I. Gutman, On leap Zagreb indices of graphs, Commun. Comb. Optim., 2017, 2, 99–117], which were named as the Zagreb connection indices and the leap Zagreb indices, respectively. In this paper, we derive formulas for calculating these modified versions of the Zagreb indices of four well known nanostructures.

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The QSPR Study of Butane derivatives: (A Mathematical Approach)

Oriental Journal Of Chemistry ◽

10.13005/ojc/3404018 ◽

2018 ◽

Vol 34 (4) ◽

pp. 1842-1846

Author(s):

Anjusha Asok ◽

Joseph Varghese Kureethara

Keyword(s):

Close Correlation ◽

Topological Indices ◽

First Zagreb Index ◽

Qspr Model ◽

Zagreb Index ◽

Hydrogen Bond Acceptor ◽

Physiochemical Properties ◽

Qspr Study ◽

Structural Insight ◽

Insight Into

The QSPR analysis provides a significant structural insight into the physiochemical properties of Butane derivatives. We study some physiochemical properties of fourteen Butane derivatives and develop a QSPR model using four topological indices and Butane derivatives. Here we analyze how closely the topological indices are related to the physiochemical properties of Butane derivatives. For this we compute analytically the topological indices of Butane derivatives and plot the graphs between each of these topological indices to the properties of Butane derivatives using Origin. This QSPR model exhibits a close correlation between Heavy atomic count, Complexity, Hydrogen bond acceptor count, and Surface tension of Butane derivatives with the Redefined first Zagreb index, the Redefined third Zagreb index, the Sum connectivity index and the Reformulated first Zagreb index, respectively.

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

International Journal of Mathematics for Industry ◽

10.1142/s2661335219500060 ◽

2019 ◽

Vol 11 (01) ◽

pp. 1950006 ◽

Cited By ~ 2

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.

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