scholarly journals On the Inverse Problem for Some Topological Indices

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Durbar Maji ◽  
Ganesh Ghorai ◽  
Muhammad Khalid Mahmood ◽  
Md. Ashraful Alam
Keyword(s):  
Inverse Problem ◽  
Topological Indices ◽  
Negative Integer ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Molecular Tree ◽  
Bicyclic Graphs

The study of the inverse problem (IP) based on the topological indices (TIs) deals with the numerical relations to TIs. Mathematically, the IP can be expressed as follows: given a graph parameter/TI that assigns a non-negative integer value g to every graph within a given family G of graphs, find some G ∈ G for which TI G = g . It was initiated by the Zefirov group in Moscow and later Gutman et al. proposed it. In this paper, we have established the IP only for the Y -index, Gourava indices, second hyper-Zagreb index, reformulated first Zagreb index, and reformulated F -index since they are closely related to each other. We have also studied the same which is true for the molecular, tree, unicyclic, and bicyclic graphs.

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

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.

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.

A Novel Weighted First Zagreb Index of Graph

2020 ◽  
pp. 92-103
Author(s):  
Jibonjyoti Buragohain ◽  
A. Bharali
Keyword(s):  
Connected Graph ◽  
Chemical Properties ◽  
Topological Indices ◽  
First Zagreb Index ◽  
Acentric Factor ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Physico Chemical ◽  
Octane Isomers ◽  
The First Zagreb Index

The Zagreb indices are the oldest among all degree-based topological indices. For a connected graph G, the first Zagreb index M1(G) is the sum of the term dG(u)+dG(v) corresponding to each edge uv in G, that is, M1 , where dG(u) is degree of the vertex u in G. In this chapter, the authors propose a weighted first Zagreb index and calculate its values for some standard graphs. Also, the authors study its correlations with various physico-chemical properties of octane isomers. It is found that this novel index has strong correlation with acentric factor and entropy of octane isomers as compared to other existing topological indices.

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

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 271 ◽  
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 .

Degree-based topological indices of double graphs and strong double graphs

2017 ◽  
Vol 09 (05) ◽  
pp. 1750066 ◽  
Author(s):  
Muhammad Imran ◽  
Shehnaz Akhter
Keyword(s):  
Graph Theory ◽  
Physicochemical Properties ◽  
Boiling Point ◽  
Strain Energy ◽  
Chemical Compounds ◽  
Topological Indices ◽  
First Zagreb Index ◽  
Original Graph ◽  
Zagreb Index ◽  
Zagreb Indices

The topological indices are useful tools to the theoretical chemists that are provided by the graph theory. They correlate certain physicochemical properties such as boiling point, strain energy, stability, etc. of chemical compounds. For a graph [Formula: see text], the double graph [Formula: see text] is a graph obtained by taking two copies of graph [Formula: see text] and joining each vertex in one copy with the neighbors of corresponding vertex in another copy and strong double graph SD[Formula: see text] of the graph [Formula: see text] is the graph obtained by taking two copies of the graph [Formula: see text] and joining each vertex [Formula: see text] in one copy with the closed neighborhood of the corresponding vertex in another copy. In this paper, we compute the general sum-connectivity index, general Randi[Formula: see text] index, geometric–arithmetic index, general first Zagreb index, first and second multiplicative Zagreb indices for double graphs and strong double graphs and derive the exact expressions for these degree-base topological indices for double graphs and strong double graphs in terms of corresponding index of original graph [Formula: see text].

scholarly journals Topological Indices of Some New Graph Operations and Their Possible Applications

2021 ◽  
pp. 16-30
Author(s):  
Abdu Qaid Saif Alameri ◽  
Mohammed Saad Yahya Al-Sharafi
Keyword(s):  
Graph Theory ◽  
Chemical Compounds ◽  
Topological Indices ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Structural Invariant ◽  
Graph Operations ◽  
Chemical Graph Theory ◽  
Cyclic Alkanes ◽  
The First Zagreb Index

A chemical graph theory is a fascinating branch of graph theory which has many applications related to chemistry. A topological index is a real number related to a graph, as its considered a structural invariant. It’s found that there is a strong correlation between the properties of chemical compounds and their topological indices. In this paper, we introduce some new graph operations for the first Zagreb index, second Zagreb index and forgotten index "F-index". Furthermore, it was found some possible applications on some new graph operations such as roperties of molecular graphs that resulted by alkanes or cyclic alkanes.

scholarly journals Relations between ordinary and multiplicative degree-based topological indices

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 3031-3042 ◽  
Author(s):  
Ivan Gutman ◽  
Igor Milovanovic ◽  
Emina Milovanovic
Keyword(s):  
Lower Bounds ◽  
Connected Graph ◽  
Topological Indices ◽  
Upper And Lower Bounds ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Vertex Degrees ◽  
Simple Connected Graph

Let G be a simple connected graph with n vertices and m edges, and sequence of vertex degrees d1 ? d2 ?...? dn > 0. If vertices i and j are adjacent, we write i ~ j. Denote by ?1, ?*1, Q? and H? the multiplicative Zagreb index, multiplicative sum Zagreb index, general first Zagreb index, and general sumconnectivity index, respectively. These indices are defined as ?1 = ?ni=1 d2i, ?*1 = ?i~j(di+dj), Q? = ?n,i=1 d?i and H? = ?i~j(di+dj)?. We establish upper and lower bounds for the differences H?-m (?1*)?/m and Q?-n(?1)?/2n . In this way we generalize a number of results that were earlier reported in the literature.

scholarly journals Topological Study of Zeolite Socony Mobil-5 via Degree-Based Topological Indices

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Nouman Saeed ◽  
Kai Long ◽  
Tanweer Ul Islam ◽  
Zeeshan Saleem Mufti ◽  
Ayesha Abbas
Keyword(s):  
Graph Theory ◽  
Melting Point ◽  
Topological Index ◽  
Hydrophobic Surface ◽  
Topological Indices ◽  
Discrete Mathematics ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Point Density ◽  
Abc Index

Graph theory is a subdivision of discrete mathematics. In graph theory, a graph is made up of vertices connected through edges. Topological indices are numerical parameters or descriptors of graph. Topological index tells the symmetry of compound and helps us to compare those mathematical values, with boiling point, melting point, density, viscosity, hydrophobic surface area, polarity, etc., of that compound. In the present research paper, degree-based topological indices of Zeolite Socony Mobil-5 are calculated. Names of those topological indices are Randić index, first Zagreb index, general sum connectivity index, hyper-Zagreb index, geometric index, ABC index, etc.

scholarly journals Zagreb Connection Indices of Two Dendrimer Nanostars

2019 ◽  
Vol 27 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Nisar Fatima ◽  
Akhlaq Ahmad Bhatti ◽  
Akbar Ali ◽  
Wei Gao
Keyword(s):  
Molecular Structure ◽  
Physicochemical Properties ◽  
Chemical Compounds ◽  
Topological Indices ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Mathematical Chemistry ◽  
Octane Isomers ◽  
The First Zagreb Index

Abstract It is well known fact that several physicochemical properties of chemical compounds are closely related to their molecular structure. Mathematical chemistry provides a method to predict the aforementioned properties of compounds using topological indices. The Zagreb indices are among the most studied topological indices. Recently, three modified versions of the Zagreb indices were proposed independently in [Ali, A.; Trinajstić, N. A novel/old modification of the first Zagreb index, arXiv:1705.10430 [math.CO] 2017; Mol. Inform. 2018, 37, 1800008] and [Naji, A. M.; Soner, N. D.; Gutman, I. 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 check the chemical applicability of the newly considered Zagreb connection indices on the set of octane isomers and establish general expressions for calculating these indices of two well-known dendrimer nanostars.

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

2014 ◽  
Vol 31 ◽  
pp. 56-62 ◽  
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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