Use of symmetry plane fragmentation and graph squaring techniques to express the eigenspectra for some vertex-weighted graphs of linear chains and cycles in analytical form

Abstract

Three types of graphs of linear chains, viz. linear chains with unit increment or decrement in weight on one terminal vertex, linear chains with unit increment or decrement in weight on both the terminal vertices and linear chains with unit increment in weight on one terminal vertex and decrement in that on the other terminal vertex, have been considered. The symmetry plane fragmentation and graph squaring techniques have been exploited to express the eigenspectra of such graphs of linear chains in analytical form, and have subsequently been used to express the eigenspectra of graphs of linear chains and cycles with alternant vertex weights. The derived expressions for the eigenspectra have been used to obtain the eigenspectra of linear polyacenes, methylene-substituted linear polyacenes and cylindrical polyacene strips in analytical form.