General (α, 2)-path sum-connectivirty indices of one important class of polycyclic aromatic hydrocarbons

Abstract

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 a and arbitrary positive integer t, it is defined as tχα(G) = ΣPt=υi1 υi2·υit+1 ⊇G[dG(υi1 )dG(υi2 )···dG(υit+1)]α, where we take the sum over all possible paths of length t of G and two paths υi1υi2···υit+1 and υit+1·vi2vi1 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.