The General (α,3)-Path Connectivity Indices of Polycyclic Aromatic Hydrocarbons
The general (α,t)-path connectivity index of a molecular graph originates from many practical problems such as three-dimensional quantitative structure-activity (3D QSAR) and molecular chirality. It is defined as Rtα(G)=∑Pt=vi1vi2⋯vit+1⊆G[d(vi1)d(vi2)⋯d(vit+1)]α, where the summation is taken over al...
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| Format: | Article |
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Wiley
2018-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/5702346 |
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| author | Haiying Wang Chuantao Li |
| author_facet | Haiying Wang Chuantao Li |
| author_sort | Haiying Wang |
| collection | DOAJ |
| description | The general (α,t)-path connectivity index of a molecular graph originates from many practical problems such as three-dimensional quantitative structure-activity (3D QSAR) and molecular chirality. It is defined as Rtα(G)=∑Pt=vi1vi2⋯vit+1⊆G[d(vi1)d(vi2)⋯d(vit+1)]α, where the summation is taken over all possible paths of length t of G and we do not distinguish between the paths vi1vi2⋯vit+1 and vit+1⋯vi2vi1. In this paper, we focus on the structures of Polycyclic Aromatic Hydrocarbons (PAHn), which play a role in organic materials and medical sciences. We try to compute the exact general (α,3)-path connectivity indices of this family of hydrocarbon structures. Furthermore, we exactly derive the monotonicity and the extremal values of R3α(PAHn) for any real number α. These valuable results could produce strong guiding significance to these applied sciences. |
| format | Article |
| id | doaj-art-4a77994dc43742b1be1d2addb925b828 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-4a77994dc43742b1be1d2addb925b8282025-02-03T01:24:05ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/57023465702346The General (α,3)-Path Connectivity Indices of Polycyclic Aromatic HydrocarbonsHaiying Wang0Chuantao Li1School of Science, China University of Geosciences (Beijing), Beijing, 100083, ChinaSchool of Science, China University of Geosciences (Beijing), Beijing, 100083, ChinaThe general (α,t)-path connectivity index of a molecular graph originates from many practical problems such as three-dimensional quantitative structure-activity (3D QSAR) and molecular chirality. It is defined as Rtα(G)=∑Pt=vi1vi2⋯vit+1⊆G[d(vi1)d(vi2)⋯d(vit+1)]α, where the summation is taken over all possible paths of length t of G and we do not distinguish between the paths vi1vi2⋯vit+1 and vit+1⋯vi2vi1. In this paper, we focus on the structures of Polycyclic Aromatic Hydrocarbons (PAHn), which play a role in organic materials and medical sciences. We try to compute the exact general (α,3)-path connectivity indices of this family of hydrocarbon structures. Furthermore, we exactly derive the monotonicity and the extremal values of R3α(PAHn) for any real number α. These valuable results could produce strong guiding significance to these applied sciences.http://dx.doi.org/10.1155/2018/5702346 |
| spellingShingle | Haiying Wang Chuantao Li The General (α,3)-Path Connectivity Indices of Polycyclic Aromatic Hydrocarbons Discrete Dynamics in Nature and Society |
| title | The General (α,3)-Path Connectivity Indices of Polycyclic Aromatic Hydrocarbons |
| title_full | The General (α,3)-Path Connectivity Indices of Polycyclic Aromatic Hydrocarbons |
| title_fullStr | The General (α,3)-Path Connectivity Indices of Polycyclic Aromatic Hydrocarbons |
| title_full_unstemmed | The General (α,3)-Path Connectivity Indices of Polycyclic Aromatic Hydrocarbons |
| title_short | The General (α,3)-Path Connectivity Indices of Polycyclic Aromatic Hydrocarbons |
| title_sort | general α 3 path connectivity indices of polycyclic aromatic hydrocarbons |
| url | http://dx.doi.org/10.1155/2018/5702346 |
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