Armchair Polyhex Nanotubes Research Articles

On Alpha and Gamma Gourava Indices

In this paper, we introduce the alpha Gourava and gamma Gourava indices of a graph. Also we compute the alpha and gamma Gourava indices of some standard graphs, armchair polyhex nanotubes and zigzag polyhex nanotubes

Multiplicative Atom Bond Sum Connectivity Index of Certain Nanotubes

We put forward the multiplicative atom bond sum connectivity index of a graph. We determine the atom bond sum connectivity index and the multiplicative atom bond sum connectivity index for some chemical nanostructures such as armchair polyhex nanotubes, zigzag polyhex nanotubes and carbon nanocone networks.

Analyzing the expressions for nanostructures via topological indices

In molecular science, one of the key problem is to model a chemical compound and predict its chemical characteristic. Numerous hypothetical methods have been created by various analysts in this respect and one of them is concerned with the topological indices. A topological index is a numerical value attached with the structural graph of a molecule and is expected to predict certain chemical/physical properties of molecule [6]. Among the classes of topological indices, degree based topological indices play a vital role in chemical graph theory. In the current study, we compute the neighborhood second Zagreb index and the first extended first–order connectivity index of Planar zigzag nanotube PTUZC 6 , polyhex zigzag nanotube H 2 = TUZC 6 , polyhex zigzag nanotori TTUZC 6 , C 4 C 8 ( S ) [ m , n ] nanosheets, C 4 C 8 ( S ) [ m , n ] nanotubes, C 4 C 8 ( S ) [ m , n ] nanotori and armchair polyhex nanotubes TUAC 6 [ p , q ] .

Szeged Related Indices of TUAC6[p, q

As an irrepressible distance-based topological indices, the Szeged related indices, it illustrates certain structural and chemical characteristics of organic molecules. Here, based on the molecular structural analysis, we present the Szeged polynomial, revised Szeged index and normalized revised Szeged index of armchair polyhex nanotubes.

The General Connectivity and General Sum-Connectivity Indices of Nanostructures

Let G be a simple graph with vertex set V(G) and edge set E(G). For ∀νi∈V(G),di denotes the degree of νi in G. The Randić connectivity index of the graph G is defined as [1-3] χ(G)=∑e=v1v2є(G)(d1d2)-1/2. The sum-connectivity index is defined as χ(G)=∑e=v1v2є(G)(d1+d2)-1/2. The sum-connectivity index is a new variant of the famous Randić connectivity index usable in quantitative structure-property relationship and quantitative structure-activity relationship studies. The general m-connectivety and general m-sum connectivity indices of G are defined as mχ(G)=∑e=v1v2...vim+1(1/√(di1di2...dim+1)) and mχ(G)=∑e=v1v2...vim+1(1/√(di1+di2+...+dim+1)) where vi1vi2...vim+1 runs over all paths of length m in G. In this paper, we introduce a closed formula of the third-connectivity index and third-sum-connectivity index of nanostructure "Armchair Polyhex Nanotubes TUAC6[m,n]" (m,n≥1).

The General Connectivity and General Sum-Connectivity Indices of Nanostructures

Let G be a simple graph with vertex set V(G) and edge set E(G). For ∀νi∈V(G),di denotes the degree of νi in G. The Randić connectivity index of the graph G is defined as [1-3] χ(G)=∑e=v1v2є(G)(d1d2)-1/2. The sum-connectivity index is defined as χ(G)=∑e=v1v2є(G)(d1+d2)-1/2. The sum-connectivity index is a new variant of the famous Randić connectivity index usable in quantitative structure-property relationship and quantitative structure-activity relationship studies. The general m-connectivety and general m-sum connectivity indices of G are defined as mχ(G)=∑e=v1v2...vim+1(1/√(di1di2...dim+1)) and mχ(G)=∑e=v1v2...vim+1(1/√(di1+di2+...+dim+1)) where vi1vi2...vim+1 runs over all paths of length m in G. In this paper, we introduce a closed formula of the third-connectivity index and third-sum-connectivity index of nanostructure "Armchair Polyhex Nanotubes TUAC6[m,n]" (m,n≥1).

On the SD-Polynomial and SD-Index of an Infinite Class of “Armchair Polyhex Nanotubes”

Let G be a simple connected graph with the vertex set V = V(G) and the edge set E = E(G),without loops and multiple edges. For counting qoc strips in G, Diudea introduced the Ω-polynomialof G and was defined as Ω(G, x) = ∑ki-1xi where C1, C2,..., Ck be the “opposite edge strips” ops of Gand ci = |Ci| (I = 1, 2,..., k). One can obtain the Sd-polynomial by replacing xc with x|E(G)|-c in Ω-polynomial. Then the Sd-index will be the first derivative of Sd(x) evaluated at x = 1. In this paper wecompute the Sd-polynomial and Sd-index of an infinite class of “Armchair Polyhe x Nanotubes”.

The Second-Connectivity and Second-Sum-Connectivity Indices of Armchair Polyhex Nanotubes TUAC<sub>6</sub>[m,n

The m-connectivety and m-sum connectivity indices of G are defined as to be and where runs over all paths of length m in G and di is the degree of vertex νi. In this paper, we give explicit formulas for the second-connectivity and second-sum-connectivity indices of an infinite class of Armchair Polyhex Nanotubes TUAC6[m,n].

On the SD-Polynomial and SD-Index of an Infinite Class of “Armchair Polyhex Nanotubes”

Let G be a simple connected graph with the vertex set V = V(G) and the edge set E = E(G),without loops and multiple edges. For counting qoc strips in G, Diudea introduced the Ω-polynomialof G and was defined as Ω(G, x) = ∑ki-1xi where C1, C2,..., Ck be the “opposite edge strips” ops of Gand ci = |Ci| (I = 1, 2,..., k). One can obtain the Sd-polynomial by replacing xc with x|E(G)|-c in Ω-polynomial. Then the Sd-index will be the first derivative of Sd(x) evaluated at x = 1. In this paper wecompute the Sd-polynomial and Sd-index of an infinite class of “Armchair Polyhe x Nanotubes”.

The Second-Connectivity and Second-Sum-Connectivity Indices of Armchair Polyhex Nanotubes TUAC<sub>6</sub>[m,n

The m-connectivety and m-sum connectivity indices of G are defined as to be and where runs over all paths of length m in G and di is the degree of vertex νi. In this paper, we give explicit formulas for the second-connectivity and second-sum-connectivity indices of an infinite class of Armchair Polyhex Nanotubes TUAC6[m,n].

The Third Geometric-Arithmetic Index of Armchair Polyhex Nanotubes

The Third Geometric-Arithmetic Index of Armchair Polyhex Nanotubes

Applications of the Matrix Package MATLAB in Computing the Wiener Polynomial of Armchair Polyhex Nanotubes and Nanotori

Applications of the Matrix Package MATLAB in Computing the Wiener Polynomial of Armchair Polyhex Nanotubes and Nanotori

Topological Relationship Between Wiener, Padmaker‐Ivan, and Szeged Indices and Energy and Electric Moments in Armchair Polyhex Nanotubes with the Same Circumference and Varying Lengths

Carbon nanotubes are carbon nanostructure compounds that have been synthesized and identified in an attractive array of structures and forms. Graph theory is a branch of mathematics related to topology and combinatorial problems. Chemical graph theory has been extensively applied to predicting the physical properties of small molecules through quantitative structure‐property relationships (QSPRs). A large number of topographical indices (TIs) have been reported, and strong correlations have been demonstrated between many physical properties and one or more topological indices. In this study, relationships are presented between topological indices such as the Wiener, Padmakar‐Ivan and Szeged indices, and the electric moments and energies (kJmol−1) of some armchair polyhex carbon nanotubes TUVC6[2p,q] with a fixed circumference [2p] and various lengths [q]. The results are performed by Becke's 3‐parameter formulation with the Lee‐Yang‐Parr functional (B3LYP) method on the 3‐21G basis set.

The Modified Schultz Index of Armchair Polyhex Nanotubes

The Modified Schultz Index of Armchair Polyhex Nanotubes

Schultz index of armchair polyhex nanotubes.

The study of topological indices – graph invariants that can be used for describing and predicting physicochemical or pharmacological properties of organic compounds – is currently one of the most active research fields in chemical graph theory. In this paper we study the Schultz index and find a relation with the Wiener index of the armchair polyhex nanotubes TUV C6[2p; q]. An exact expression for Schultz index of this molecule is also found.