The General (α, 3)-Path Connectivity Indices of Polycyclic Aromatic Hydrocarbons. (5th September 2018) - Wang, Haiying; Li, Chuantao
Abstract : 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 asR t α ( G ) = ∑ P t = v i 1 v i 2 ⋯ v i t + 1 ⊆ G [ d ( v i 1 ) d ( v i 2 ) ⋯ d ( v i t + 1 ) ] α, where the summation is taken over all possible paths of lengtht ofG and we do not distinguish between the pathsv i 1 v i 2 ⋯ v i t + 1 andv i t + 1 ⋯ v i 2 v i 1 . In this paper, we focus on the structures of Polycyclic Aromatic Hydrocarbons (P A H n ), 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 ofR 3 α ( P A H n ) for any real numberα . These valuable results could produce strong guiding significance to these applied sciences.