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Open AccessArticle

General (α,2)-Path Sum-Connectivirty Indices of One Important Class of Polycyclic Aromatic Hydrocarbons

School of Science, China University of Geosciences (Beijing), Beijing 100083, China
Symmetry 2018, 10(10), 426; https://doi.org/10.3390/sym10100426
Received: 14 August 2018 / Revised: 5 September 2018 / Accepted: 6 September 2018 / Published: 21 September 2018
(This article belongs to the Special Issue Symmetry in Graph Theory)
The general ( α , t ) -path sum-connectivity index of a molecular graph originates from many practical problems, such as the three-dimensional quantitative structure–activity relationships (3D QSAR) and molecular chirality. For arbitrary nonzero real number α and arbitrary positive integer t, it is defined as t χ α ( G ) = P t = v i 1 v i 2 v i t + 1 G [ d G ( v i 1 ) d G ( v i 2 ) d G ( v i t + 1 ) ] α , where we take the sum over all possible paths of length t of G and two paths v i 1 v i 2 v i t + 1 and v i t + 1 v i 2 v i 1 are considered to be one path. In this work, one important class of polycyclic aromatic hydrocarbons and their structures are firstly considered, which play a role in organic materials and medical sciences. We try to compute the exact general ( α , 2 ) -path sum-connectivity indices of these hydrocarbon systems. Furthermore, we exactly derive the monotonicity and the extremal values of these polycyclic aromatic hydrocarbons for any real number α . These valuable results could produce strong guiding significance to these applied sciences. View Full-Text
Keywords: topological indices; general (α,t)-path sum-connectivity index; polycyclic aromatic hydrocarbons topological indices; general (α,t)-path sum-connectivity index; polycyclic aromatic hydrocarbons
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MDPI and ACS Style

Wang, H. General (α,2)-Path Sum-Connectivirty Indices of One Important Class of Polycyclic Aromatic Hydrocarbons. Symmetry 2018, 10, 426. https://doi.org/10.3390/sym10100426

AMA Style

Wang H. General (α,2)-Path Sum-Connectivirty Indices of One Important Class of Polycyclic Aromatic Hydrocarbons. Symmetry. 2018; 10(10):426. https://doi.org/10.3390/sym10100426

Chicago/Turabian Style

Wang, Haiying. 2018. "General (α,2)-Path Sum-Connectivirty Indices of One Important Class of Polycyclic Aromatic Hydrocarbons" Symmetry 10, no. 10: 426. https://doi.org/10.3390/sym10100426

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