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 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 Multiplicative Zagreb Indices of Molecular Graphs

2019 ◽  
Vol 2019 ◽  
pp. 1-19 ◽  
Author(s):  
Xiujun Zhang ◽  
H. M. Awais ◽  
M. Javaid ◽  
Muhammad Kamran Siddiqui
Keyword(s):  
Mathematical Modeling ◽  
Vital Role ◽  
Molecular Structures ◽  
Quantitative Structure ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Molecular Graphs ◽  
Structure Properties

Mathematical modeling with the help of numerical coding of graphs has been used in the different fields of science, especially in chemistry for the studies of the molecular structures. It also plays a vital role in the study of the quantitative structure activities relationship (QSAR) and quantitative structure properties relationship (QSPR) models. Todeshine et al. (2010) and Eliasi et al. (2012) defined two different versions of the 1st multiplicative Zagreb index as ∏Γ=∏p∈VΓdΓp2 and ∏1Γ=∏pq∈EΓdΓp+dΓq, respectively. In the same paper of Todeshine, they also defined the 2nd multiplicative Zagreb index as ∏2Γ=∏pq∈EΓdΓp×dΓq. Recently, Liu et al. [IEEE Access; 7(2019); 105479–-105488] defined the generalized subdivision-related operations of graphs and obtained the generalized F-sum graphs using these operations. They also computed the first and second Zagreb indices of the newly defined generalized F-sum graphs. In this paper, we extend this study and compute the upper bonds of the first multiplicative Zagreb and second multiplicative Zagreb indices of the generalized F-sum graphs. At the end, some particular results as applications of the obtained results for alkane are also included.

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 On Multiple Zagreb Indices of Dendrimer Nanostars

2015 ◽  
Vol 52 ◽  
pp. 147-151 ◽  
Author(s):  
Mohammad Reza Farahani
Keyword(s):  
Topological Indices ◽  
Infinite Class ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Degree Of A Vertex

In this paper, we focus on the structure of an infinite class of Dendrimer Nanostars D3[n] (n≥0 is infinite integer) and counting its First Multiple Zagreb index and Second Multiple Zagreb index. The Multiple Zagreb topological indices are equal to PM1(G)=(dv+dv) and PM2(G)=(dv×dv), where dv is the degree of a vertex v.

scholarly journals Three Topological Indices of Two New Variants of Graph Products

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Muhammad Bilal ◽  
Muhammad Kamran Jamil ◽  
Muhammad Waheed ◽  
Abdu Alameri
Keyword(s):  
Social Sciences ◽  
Complex Network ◽  
New Products ◽  
Topological Indices ◽  
Network Structures ◽  
Graph Products ◽  
Zagreb Index ◽  
Simple Graphs ◽  
Zagreb Indices ◽  
Graph Operation

Graph operations play an important role to constructing complex network structures from simple graphs, and these complex networks play vital roles in different fields such as computer science, chemistry, and social sciences. Computation of topological indices of these complex network structures via graph operation is an important task. In this study, we defined two new variants of graph products, namely, corona join and subdivision vertex join products and investigated exact expressions of the first and second Zagreb indices and first reformulated Zagreb index for these new products.

Some topological indices of dendrimers

2020 ◽  
pp. 2050018
Author(s):  
S. Alyar ◽  
R. Khoeilar ◽  
A. Jahanbani
Keyword(s):  
Graph Theory ◽  
Molecular Graph ◽  
Topological Indices ◽  
Molecular Structures ◽  
Topological Properties ◽  
Zagreb Index ◽  
Zinc Porphyrin ◽  
Molecular Graphs

There are immense applications of graph theory in chemistry and in the study of molecular structures, and after that, it has been increasing exponentially. Molecular graphs have points (vertices) representing atoms and lines (edges) that represent bonds between atoms. In this paper, we study the molecular graph of porphyrin, propyl ether imine, zinc–porphyrin and poly dendrimers and analyzed its topological properties. For this purpose, we have computed topological indices, namely the Albertson index, the sigma index, the Nano-Zagreb index, the first and second hyper [Formula: see text]-indices of porphyrin, propyl ether imine, zinc–porphyrin and poly dendrimers.

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.

On the First and Second Zagreb and First and Second Hyper-Zagreb Indices of Carbon Nanocones CNCk[n]

2016 ◽  
Vol 13 (10) ◽  
pp. 7475-7482 ◽  
Author(s):  
Wei Gao ◽  
Mohammad Reza Farahani ◽  
Muhammad Kamran Siddiqui ◽  
Muhammad Kamran Jamil
Keyword(s):  
Molecular Graph ◽  
Topological Indices ◽  
Zagreb Index ◽  
Carbon Nanocones ◽  
Zagreb Indices ◽  
Minimum Path ◽  
Multiple Edges

Let G be a simple molecular graph without directed and multiple edges and without loops, the vertex and edge-sets of which are represented by V(G) and E(G), respectively. Suppose G is a connected molecular graph and vertices u, v ∈ V(>G). The distance dG(u,v) (or d(u,v) for short) between vertices u and V of G is defined as the length of a minimum path between u and V. The first and second Zagreb indices of a graph G are defined as M1(G) = ΣE=uv∈E(G)(dV+dV) and M2(G) = ΣE=uv∈E(G)(dV×dv) where du and dv are the degree of the vertices u and V of G. Recently the Hyper-Zagreb index of a graph G is defined as HM(G) = ΣE=uv∈E(G)(dV+dV)2, by Shirdel et al. In this paper, we define a new version of Zagreb topological indices, on based the Hyper-Zagreb index that defined as the sum of the weights (dudV)2 and the Second Hyper-Zagreb index of G is equal to HM2(G) = ΣE=uv∈E(G)(dVdV)22. In continue, exact formulas for the first and second Zagreb and Hyper-Zagreb indices of Carbon Nanocones CNCk[n] are computed.

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].

THE THIRD VERSION OF ZAGREB INDEX

2013 ◽  
Vol 05 (04) ◽  
pp. 1350039 ◽  
Author(s):  
MODJTABA GHORBANI ◽  
MOHAMMAD A. HOSSEINZADEH
Keyword(s):  
Topological Indices ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
The Third ◽  
First Time

Gutman et al. defined the Zagreb indices for the first time more than 40 years ago and up to now many versions of these topological indices were defined. In this paper we define a type of Zagreb indices based on degrees of neighbors of vertices in a given graph and then we compute them for several classes of composite graphs.

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