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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 χα(G) = Pt=vi1 vi2 ···vit+1⊆G [dG(vi1)dG(vi2) · · · dG(vit+1)] α, where we take the sum over all possible paths of length t of G and two paths vi1 vi2 · · · vit+1 and vit+1 · · · vi2 vi1 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.

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