scholarly journals The first general Zagreb coindex of graph operations

2020 ◽  
Vol 5 (2) ◽  
pp. 109-120
Author(s):  
Melaku Berhe Belay ◽  
Chunxiang Wang
Keyword(s):  
Tensor Product ◽  
Cartesian Product ◽  
Molecular Graphs ◽  
Basic Properties ◽  
Graph Operations ◽  
Nano Structures ◽  
Product Composition ◽  
Product Of Graphs

AbstractMany chemically important graphs can be obtained from simpler graphs by applying different graph operations. Graph operations such as union, sum, Cartesian product, composition and tensor product of graphs are among the important ones. In this paper, we introduce a new invariant which is named as the first general Zagreb coindex and defined as \overline{M}^\alpha_1(G)=\Sigma_{uv\in E(\overline{G})}[d_G(u)^\alpha+d_G(v)^\alpha] , where α ∈ ℝ, α ≠ 0. Here, we study the basic properties of the newly introduced invariant and its behavior under some graph operations such as union, sum, Cartesian product, composition and tensor product of graphs and hence apply the results to find the first general Zagreb coindex of different important nano-structures and molecular graphs.

scholarly journals Upper Bounds for the Modified Second Multiplicative Zagreb Index of Graph Operations

2016 ◽  
Vol 17 ◽  
pp. 10-16
Author(s):  
Bommanahal Basavanagoud ◽  
Shreekant Patil
Keyword(s):  
Connected Graph ◽  
Cartesian Product ◽  
Upper Bounds ◽  
Zagreb Index ◽  
Graph Operations ◽  
Product Composition ◽  
Degree Of A Vertex ◽  
Product Of Graphs ◽  
Corona Product

The modified second multiplicative Zagreb index of a connected graph G, denoted by $\prod_{2}^{*}(G)$, is defined as $\prod_{2}^{*}(G)=\prod \limits_{uv\in E(G)}[d_{G}(u)+d_{G}(v)]^{[d_{G}(u)+d_{G}(v)]}$ where $d_{G}(z)$ is the degree of a vertex z in G. In this paper, we present some upper bounds for the modified second multiplicative Zagreb index of graph operations such as union, join, Cartesian product, composition and corona product of graphs are derived.The modified second multiplicative Zagreb index of aconnected graph , denoted by , is defined as where is the degree of avertex in . In this paper, we present some upper bounds for themodified second multiplicative Zagreb index of graph operations such as union,join, Cartesian product, composition and corona product of graphs are derived.

scholarly journals HF-Index and Y-Index of Some New Graph of Operations

2022 ◽  
pp. 28-33
Author(s):  
Dr. S. Nagarajan ◽  
◽  
G. Kayalvizhi ◽  
G. Priyadharsini ◽  
◽  
...  
Keyword(s):  
Cartesian Product ◽  
Graph Operations ◽  
Join Of Graphs ◽  
Product Of Graphs ◽  
Corona Product

In this paper we derive HF index of some graph operations containing join, Cartesian Product, Corona Product of graphs and compute the Y index of new operations of graphs related to the join of graphs.

scholarly journals The Second Hyper-Zagreb Coindex of Chemical Graphs and Some Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Ahmed Ayache ◽  
Abdu Alameri ◽  
Mohammed Alsharafi ◽  
Hanan Ahmed
Keyword(s):  
Tensor Product ◽  
Topological Index ◽  
Molecular Graph ◽  
Cartesian Product ◽  
Explicit Formulas ◽  
Chemical Graph ◽  
Strong Product ◽  
Chemical Graphs ◽  
Product Composition ◽  
Graph Structures

The second hyper-Zagreb coindex is an efficient topological index that enables us to describe a molecule from its molecular graph. In this current study, we shall evaluate the second hyper-Zagreb coindex of some chemical graphs. In this study, we compute the value of the second hyper-Zagreb coindex of some chemical graph structures such as sildenafil, aspirin, and nicotine. We also present explicit formulas of the second hyper-Zagreb coindex of any graph that results from some interesting graphical operations such as tensor product, Cartesian product, composition, and strong product, and apply them on a q-multiwalled nanotorus.

A novel graph invariant: The third leap Zagreb index under several graph operations

2019 ◽  
Vol 11 (05) ◽  
pp. 1950054 ◽  
Author(s):  
Durbar Maji ◽  
Ganesh Ghorai
Keyword(s):  
Tensor Product ◽  
Cartesian Product ◽  
Lexicographic Product ◽  
Graph Invariant ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
The Third ◽  
Graph Operations ◽  
Strong Product ◽  
Corona Product

The third leap Zagreb index of a graph [Formula: see text] is denoted as [Formula: see text] and is defined as [Formula: see text], where [Formula: see text] and [Formula: see text] are the 2-distance degree and the degree of the vertex [Formula: see text] in [Formula: see text], respectively. The first, second and third leap Zagreb indices were introduced by Naji et al. [A. M. Naji, N. D. Soner and I. Gutman, On leap Zagreb indices of graphs, Commun. Combin. Optim. 2(2) (2017) 99–117] in 2017. In this paper, the behavior of the third leap Zagreb index under several graph operations like the Cartesian product, Corona product, neighborhood Corona product, lexicographic product, strong product, tensor product, symmetric difference and disjunction of two graphs is studied.

scholarly journals The Sigma Coindex of Graph Operations

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Yasar Nacaroglu
Keyword(s):  
Tensor Product ◽  
Cartesian Product ◽  
Lexicographic Product ◽  
Nonadjacent Vertex ◽  
Graph Operations ◽  
Strong Product ◽  
Mathematical Properties ◽  
Corona Product

The sigma coindex is defined as the sum of the squares of the differences between the degrees of all nonadjacent vertex pairs. In this paper, we propose some mathematical properties of the sigma coindex. Later, we present precise results for the sigma coindices of various graph operations such as tensor product, Cartesian product, lexicographic product, disjunction, strong product, union, join, and corona product.

scholarly journals Sharp Bounds for the Inverse Sum Indeg Index of Graph Operations

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Anam Rani ◽  
Muhammad Imran ◽  
Usman Ali
Keyword(s):  
Tensor Product ◽  
Physicochemical Properties ◽  
Cartesian Product ◽  
Total Surface Area ◽  
Sharp Bounds ◽  
Graph Operations ◽  
Strong Product ◽  
Octane Isomers ◽  
International Academy ◽  
Corona Product

Vukičević and Gasperov introduced the concept of 148 discrete Adriatic indices in 2010. These indices showed good predictive properties against the testing sets of the International Academy of Mathematical Chemistry. Among these indices, twenty indices were taken as beneficial predictors of physicochemical properties. The inverse sum indeg index denoted by ISI G k of G k is a notable predictor of total surface area for octane isomers and is presented as ISI G k = ∑ g k g k ′ ∈ E G k d G k g k d G k g k ′ / d G k g k + d G k g k ′ , where d G k g k represents the degree of g k ∈ V G k . In this paper, we determine sharp bounds for ISI index of graph operations, including the Cartesian product, tensor product, strong product, composition, disjunction, symmetric difference, corona product, Indu–Bala product, union of graphs, double graph, and strong double graph.

scholarly journals F-Index of some graph operations

2016 ◽  
Vol 08 (02) ◽  
pp. 1650025 ◽  
Author(s):  
Nilanjan De ◽  
Sk. Md. Abu Nayeem ◽  
Anita Pal
Keyword(s):  
Electron Energy ◽  
Topological Index ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Molecular Graphs ◽  
Basic Properties ◽  
Graph Operations ◽  
Physico Chemical ◽  
Vertex Degrees

The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph. This was introduced in 1972, in the same paper where the first and second Zagreb indices were introduced to study the structure-dependency of total [Formula: see text]-electron energy. But this topological index was not further studied till then. Very recently, Furtula and Gutman [A forgotten topological index,J. Math. Chem. 53(4) (2015) 1184–1190.] reinvestigated the index and named it “forgotten topological index” or “F-index”. In that paper, they present some basic properties of this index and showed that this index can enhance the physico-chemical applicability of Zagreb index. Here, we study the behavior of this index under several graph operations and apply our results to find the F-index of different chemically interesting molecular graphs and nanostructures.

scholarly journals The Reciprocal Complementary Wiener Number of Graph Operations

2021 ◽  
Vol 45 (01) ◽  
pp. 139-154
Author(s):  
R. NASIRI ◽  
A. NAKHAEI ◽  
A. R. SHOJAEIFARD
Keyword(s):  
Connected Graph ◽  
Cartesian Product ◽  
Symmetric Difference ◽  
Graph Operations ◽  
Strong Product ◽  
Product Composition ◽  
Wiener Number ◽  
Corona Product

The reciprocal complementary Wiener number of a connected graph G is defined as ∑ {x,y}⊆V (G) 1 D+1-−-dG(x,y), where D is the diameter of G and dG(x,y) is the distance between vertices x and y. In this work, we study the reciprocal complementary Wiener number of various graph operations such as join, Cartesian product, composition, strong product, disjunction, symmetric difference, corona product, splice and link of graphs.

scholarly journals Adjacency Matrix of Product of Graphs

10.29007/fqlw ◽  
2018 ◽  
Author(s):  
Urvashi Acharya ◽  
Himali Mehta
Keyword(s):  
Graph Theory ◽  
Tensor Product ◽  
Adjacency Matrix ◽  
Incidence Matrix ◽  
Cartesian Product ◽  
Laplacian Matrix ◽  
New Product ◽  
Different Types ◽  
Product Of Graphs

In graph theory, different types of matrices associated with graph, e.g. Adjacency matrix, Incidence matrix, Laplacian matrix etc. Among all adjacency matrix play an important role in graph theory. Many products of two graphs as well as its generalized form had been studied, e.g., cartesian product, 2−cartesian product, tensor product, 2−tensor product etc. In this paper, we discuss the adjacency matrix of two new product of graphs G H, where = ⊗2, ×2. Also, we obtain the spectrum of these products of graphs.

Application of Corona Product of Graphs in Computing Topological Indices of Some Special Chemical Graphs

2017 ◽  
pp. 82-101
Author(s):  
Nilanjan De
Keyword(s):  
Topological Indices ◽  
Connectivity Index ◽  
Eccentric Connectivity Index ◽  
Molecular Graphs ◽  
Mathematical Chemistry ◽  
Graph Operations ◽  
Eccentricity Index ◽  
Chemical Graphs ◽  
Product Of Graphs ◽  
Corona Product

Graph operations play a very important role in mathematical chemistry, since some chemically interesting graphs can be obtained from some simpler graphs by different graph operations. In this chapter, some eccentricity based topological indices such as the total eccentricity index, eccentric connectivity index, modified eccentric connectivity index and connective eccentricity index and their respective polynomial versions of corona product of two graphs have been studied and also these indices of some important classes of chemically interesting molecular graphs are determined by specializing the components of corona product of graphs.

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