Characteristic polynomials of linear polyacenes and their subspectrality

Coefficients of characteristic polynomials (CP) of linear polyacenes (LP) have been shown to be obtainable from Pascal’s triangle by using a graph factorization and squaring technique. Strong subspectrality existing among the members of the linear polyacene series has been shown from the derivation of the CP’s. Thus it has been shown that the entire eigenspectrum of an n-ring LP is included in that of (2n + 1)-ring LP. Correspondence between the eigenspectra of linear chains and LP’s is brought out by a recently developed vertex-alternation and squaring algorithm.