Computing Sanskruti index of the Polycyclic Aromatic Hydrocarbons (original) (raw)
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Three vertex-degree-based graph invariants are presented, that earlier have been considered in the chemical and/or mathematical literature, but that evaded the attention of most mathematical chemists. These are the reciprocal Randić index (RR), the reduced second Zagreb index RM 2 , and the reduced reciprocal Randić index (RRR). If d 1 , d 2 , . . . , d n are the degrees of the vertices of the graph G = (V, E), then
Zagreb Indices and Zagreb Polynomials of Polycyclic Aromatic Hydrocarbons PAHs. [71]
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Topological indices are numerical parameters of a molecular graph G which characterize its topology. There exits many structure in graph theory, with applied in chemical and nano science and vice versa and computing the connectivity indices of molecular graphs is an important branch in chemical graph theory. In this paper, we compute First Zagreb index Zg1(G)= Second Zagreb index Zg2(G)= and their polynomials Zg1(G,x)= and Zg2(G,x)= of a family of hydrocarbon structures "Polycyclic Aromatic Hydrocarbons (PAHs)".
International Journal of Theoretical Chemistry
A topological index is a real number related to the structure of a connected graph G and is invariant under graph automorphism. Let G be a (molecular) graph possessing n vertices and m edges, and e=x,y be an edge of G and x, y are two of its vertices, then the distance d(x,y)=d(x,y|G) between the vertices x and y is equal to the length of the shortest path that connects them in G. The goal of this paper is to compute the Schultz Polynomial Modified Schultz Polynomial Hosoya Polynomial and their topological indices of first members of a family of hydrocarbon structures “Polycyclic Aromatic Hydrocarbons (PAHs)” molecular graph. Copyright © acascipub.com, all rights reserved. Keywords: Polycyclic Aromatic Hydrocarbons (PAHs), Benzenoid, Topological Indices, Wiener Index, Hosoya Polynomial, Schultz Polynomial, Modified Schultz Polynomial.
Omega and Cluj-Ilmenau Indices of Hydrocarbon Molecules “Polycyclic Aromatic Hydrocarbons PAHk”
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A topological index is a numerical value associated with chemical constitution for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. In this paper, we computed the Omega and Cluj-Ilumenau indices of a very famous hydrocarbon named as Polycyclic Aromatic Hydrocarbons k PAH for all integer number k.
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A Topological index also known as connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as Randi c ´ , atom-bond connectivity (ABC) and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study HDCN1(m,n) and HDCN2(m,n) of dimension m , n and derive analytical closed results of general Randi c ´ index R α ( G ) for different values of α . We also compute the general first Zagreb, ABC, GA, A B C 4 and G A 5 indices for these Hex derived cage networks for the first time and give closed formulas of these degree-based indices.
Computation of the fifth Geometric-Arithmetic Index for Polycyclic Aromatic Hydrocarbons PAH k
Applied Mathematics and Nonlinear Sciences, 2016
Let G be a simple connected graph. The geometric-arithmetic index of G is defined as G A 1 ( G ) = ∑ u ν ∈ E ( G ) 2 d ( u ) d ( ν ) d ( u ) + d ( ν ) beginarrayGA1left(Gright)=sumnolimitsunuinE(G)frac2sqrtd(u)d(nu)d(u)+d(nu)endarray\begin{array}{} G{A_1}\left( G \right) = {\sum\nolimits _{u\nu \in E(G)}}\frac{{2\sqrt {d(u)d(\nu)} }}{{d(u) + d(\nu)}} \end{array}beginarrayGA1left(Gright)=sumnolimitsunuinE(G)frac2sqrtd(u)d(nu)d(u)+d(nu)endarray , where d(u) represents the degree of the vertex u in the graph G. Recently, Graovac defined the fifth version of geometric-arithmetic index of a graph G as G A 5 ( G ) = ∑ u ν ∈ E ( G ) 2 S ν S u S ν + S u beginarrayGA5left(Gright)=sumnolimitsunuinE(G)frac2sqrtSnuSuSnu+Suendarray\begin{array}{} G{A_5}\left( G \right) = {\sum\nolimits _{u\nu \in E(G)}}\frac{{2\sqrt {{S_\nu}{S_u}} }}{{{S_\nu} + {S_u}}} \end{array}beginarrayGA5left(Gright)=sumnolimitsunuinE(G)frac2sqrtSnuSuSnu+Suendarray , where Su is the sum of degrees of all neighbors of vertex u in the graph G. In this paper, we compute the fifth geometric arithmetic index of Polycyclic Aromatic Hydrocarbons (PAH k ).
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A topological index, also known as connectivity index, is a molecular structure descriptor calculated from a molecular graph of a chemical compound which characterizes its topology. Various topological indices are categorized based on their degree, distance, and spectrum. In this study, we calculated and analyzed the degree-based topological indices such as first general Zagreb index M r G , geometric arithmetic index GA G , harmonic index H G , general version of harmonic index H r G , sum connectivity index λ G , general sum connectivity index λ r G , forgotten topological index F G , and many more for the Robertson apex graph. Additionally, we calculated the newly developed topological indices such as the AG 2 G and Sanskruti index for the Robertson apex graph G.