On Connectivity Indices of an Infinite Family of the Linear Parallelogram of Benzenoid Graph

The atom-bond connectivity (ABC) index is a much-studied molecular structure descriptor, based on the degrees of the vertices of the molecular graph. Recently, another vertex-degree-based topological index - the harmonic index (H) - attracted attention and gained popularity. We show how ABC and H are related.

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Fourth Atom-Bond Connectivity Index of an Infinite Class of Nanostar Dendrimer D3[n]

JOURNAL OF ADVANCES IN CHEMISTRY ◽

10.24297/jac.v12i8.2838 ◽

2016 ◽

Vol 12 (8) ◽

pp. 301-305

Author(s):

Mohammad Reza Farahani

Keyword(s):

Topological Index ◽

Connectivity Index ◽

Infinite Class ◽

Degree Of Vertex ◽

Abc Index ◽

Atom Bond

The atom-bond connectivity (ABC) index of a graph G is a connectivity topological index was defined as where dv denotes the degree of vertex v of G. In 2010, M. Ghorbani et. al. introduced a new version of atom-bond connectivity index as where In this paper, we compute a cloused formula of ABC4 index of an infinite class of Nanostar Dendrimer D3[n]. A Dendrimer is an artificially manufactured or synthesized molecule built up from branched units called monomers.

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On Molecular Descriptors of Face-Centered Cubic Lattice

Processes ◽

10.3390/pr7050280 ◽

2019 ◽

Vol 7 (5) ◽

pp. 280 ◽

Cited By ~ 6

Author(s):

Hong Yang ◽

Muhammad Aamer Rashid ◽

Sarfraz Ahmad ◽

Saima Sami Khan ◽

Muhammad Kamran Siddiqui

Keyword(s):

Cross Section ◽

Topological Index ◽

Molecular Descriptors ◽

Molecular Graph ◽

Face Centered Cubic ◽

Topological Properties ◽

Cubic Lattice ◽

Face Centered ◽

Minimal Effort ◽

Atom Bond

Face-centered cubic lattice F C C ( n ) has received extensive consideration as of late, inferable from its recognized properties and non-poisonous nature, minimal effort, plenitude, and basic creation process. The graph of a face-centered cubic cross-section contains cube points and face centres. A topological index of a molecular graph G is a numeric amount identified with G, which depicts its topological properties. In this paper, using graph theory tools, we computed the molecular descriptors (topological indices)—to be specific, Zagreb-type indices, a forgotten index, a Balaban index, the fourth version of an atom–bond connectivity index, and the fifth version of a geometric arithmetic index for face-centered cubic lattice F C C ( n ) .

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Wiener Index of Edge Thorny Graphs of Catacondensed Benzenoids

Mathematics ◽

10.3390/math8040467 ◽

2020 ◽

Vol 8 (4) ◽

pp. 467

Author(s):

Andrey A. Dobrynin ◽

Ali Iranmanesh

Keyword(s):

Polycyclic Aromatic Hydrocarbons ◽

Aromatic Hydrocarbons ◽

Topological Index ◽

Perfect Matching ◽

Molecular Graph ◽

Wiener Index ◽

Benzenoid Graph ◽

Polycyclic Aromatic ◽

Distance Properties ◽

Sum Of Distances

The Wiener index is a topological index of a molecular graph, defined as the sum of distances between all pairs of its vertices. Benzenoid graphs include molecular graphs of polycyclic aromatic hydrocarbons. An edge thorny graph G is constructed from a catacondensed benzenoid graph H by attaching new graphs to edges of a perfect matching of H. A formula for the Wiener index of G is derived. The index of the resulting graph does not contain distance characteristics of elements of H and depends on the Wiener index of H and distance properties of the attached graphs.

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The eccentric version of atom-bond connectivity index of tetra sheet networks

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830918500659 ◽

2018 ◽

Vol 10 (05) ◽

pp. 1850065 ◽

Cited By ~ 1

Author(s):

Muhammad Imran ◽

Abdul Qudair Baig ◽

Muhammad Razwan Azhar

Keyword(s):

Connected Graph ◽

Molecular Graph ◽

Theoretical Chemistry ◽

Connectivity Index ◽

Maximum Distance ◽

Eccentric Connectivity Index ◽

Topological Descriptor ◽

Degree Of A Vertex ◽

Connectivity Indices ◽

Atom Bond

Among topological descriptor of graphs, the connectivity indices are very important and they have a prominent role in theoretical chemistry. The atom-bond connectivity index of a connected graph [Formula: see text] is represented as [Formula: see text], where [Formula: see text] represents the degree of a vertex [Formula: see text] of [Formula: see text] and the eccentric connectivity index of the molecular graph [Formula: see text] is represented as [Formula: see text], where [Formula: see text] is the maximum distance between the vertex [Formula: see text] and any other vertex [Formula: see text] of the graph [Formula: see text]. The new eccentric atom-bond connectivity index of any connected graph [Formula: see text] is defined as [Formula: see text]. In this paper, we compute the new eccentric atom-bond connectivity index for infinite families of tetra sheets equilateral triangular and rectangular networks.

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Computing the Omega polynomial of an infinite family of the linear parallelogram P(n,m)

JOURNAL OF ADVANCES IN CHEMISTRY ◽

10.24297/jac.v2i2.900 ◽

2006 ◽

Vol 2 (2) ◽

pp. 106-109

Author(s):

Mohammad Reza Farahani

Keyword(s):

Molecular Graph ◽

Infinite Family ◽

Benzenoid Graph ◽

Omega Polynomial

Let G=(V,E) be a molecular graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges. The Omega polynomial Ω(G,x) was introduced by Diudea in 2006 and this defined as where m(G,c) the number of qoc strips of length c. In this paper, we compute the omega polynomial of an infinite family of the linear parallelogram P(n,n) of benzenoid graph.

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On Some Properties of Multiplicative Topological Indices in Silicon-Carbon

Journal of Mathematics ◽

10.1155/2021/4611199 ◽

2021 ◽

Vol 2021 ◽

pp. 1-10

Author(s):

Abid Mahboob ◽

Sajid Mahboob ◽

Mohammed M. M. Jaradat ◽

Nigait Nigar ◽

Imran Siddique

Keyword(s):

Graph Theory ◽

Structural Properties ◽

Topological Index ◽

Molecular Graph ◽

Chemical Compounds ◽

Google Maps ◽

Chemical Graph ◽

Zagreb Indices ◽

Silicon Carbon ◽

Connectivity Indices

The use of graph theory can be visualized in nanochemistry, computer networks, Google maps, and molecular graph which are common areas to elaborate application of this subject. In nanochemistry, a numeric number (topological index) is used to estimate the biological, physical, and structural properties of chemical compounds that are associated with the chemical graph. In this paper, we compute the first and second multiplicative Zagreb indices ( M 1 G and ( M 1 G )), generalized multiplicative geometric arithmetic index ( GA α II G ), and multiplicative sum connectivity and multiplicative product connectivity indices ( SCII G and PCII G ) of SiC 4 − I m , n and SiC 4 − II m , n .

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Computing Atom-Bond Connectivity (ABC4) index for Circumcoronene Series of Benzenoid

JOURNAL OF ADVANCES IN CHEMISTRY ◽

10.24297/jac.v2i1.910 ◽

2013 ◽

Vol 2 (1) ◽

pp. 68-72 ◽

Cited By ~ 3

Author(s):

Mohammad Reza Farahani

Keyword(s):

Connected Graph ◽

Topological Index ◽

Molecular Graph ◽

Degree Of Vertex ◽

Abc Index ◽

Simple Connected Graph ◽

Atom Bond

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. In such a simple molecular graph, vertices represent atoms and edges represent bonds. The Atom-Bond Connectivity (ABC) index is a topological index was defined as where dv denotes degree of vertex v. In 2010, a new version of Atom-Bond Connectivity (ABC4) index was defined by M. Ghorbani et. al as where and NG(u)={vV(G)|uvE(G)}. The goal of this paper is to compute the ABC4 index for Circumcoronene Series of Benzenoid

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Fourth Atom-Bond Connectivity Index of an Infinite Class of Nanostar Dendrimer D3[n]

JOURNAL OF ADVANCES IN CHEMISTRY ◽

10.24297/jac.v12i10.5521 ◽

2013 ◽

Vol 12 (10) ◽

pp. 301-305

Author(s):

Mohammad Reza Farahani

Keyword(s):

Topological Index ◽

Connectivity Index ◽

Infinite Class ◽

Degree Of Vertex ◽

Abc Index ◽

Atom Bond

The atom-bond connectivity (ABC) index of a graph G is a connectivity topological index was defined as where dv denotes the degree of vertex v of G. In 2010, M. Ghorbani et. al. introduced a new version of atom-bond connectivity index as where In this paper, we compute a cloused formula of ABC4 index of an infinite class of Nanostar Dendrimer D3[n]. A Dendrimer is an artificially manufactured or synthesized molecule built up from branched units called monomers.

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Fourth Atom-Bond Connectivity Index of an Infinite Class of Nanostar Dendrimer D3[n]

JOURNAL OF ADVANCES IN CHEMISTRY ◽

10.24297/jac.v4i1.958 ◽

2008 ◽

Vol 4 (1) ◽

pp. 301-305 ◽

Cited By ~ 1

Author(s):

Mohammad Reza Farahani

Keyword(s):

Topological Index ◽

Connectivity Index ◽

Infinite Class ◽

Degree Of Vertex ◽

Abc Index ◽

Atom Bond

The atom-bond connectivity (ABC) index of a graph G is a connectivity topological index was defined as where dv denotes the degree of vertex v of G. In 2010, M. Ghorbani et. al. introduced a new version of atom-bond connectivity index as where In this paper, we compute a cloused formula of ABC4 index of an infinite class of Nanostar Dendrimer D3[n]. A Dendrimer is an artificially manufactured or synthesized molecule built up from branched units called monomers.

Download Full-text