Method for construction of characteristic polynomials via graph linearization

Abstract

A new method for construction of characteristic polynomials (CP) of complicated graphs having arbitrary edge and vertex weights has been developed. The method first converts the graph into isospectral linear chains with weighted vertices and edges and then builds up the CP coefficients recursively. Two types of graphs have been used for illustration, viz., (i) graphs that can be linearized by symmetry factorization and (ii) graphs without symmetry which are to be linearized by an algorithm involving walks of unit length. Both types have been illustrated, of which type (i) includes the Schlegel of fullerene fragment C20 and another large graph with many fused rings. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 199–204, 1997