IJPAM: Volume 12, No. 1 (2004)

ON CHARACTERISTIC POLYNOMIALS OF
WEIGHTED MOLECULAR GRAPHS

Dietmar Dorninger$^1$, Helmut Länger$^2$
$^{1,2}$Institute of Discrete Mathematics and Geometry
Vienna University of Technology
Wiedner Hauptstraße 8-10, A-1040 Vienna, AUSTRIA
$^1$e-mail: d.dorninger@tuwien.ac.at
$^2$e-mail: h.laenger@tuwien.ac.at


Abstract.We present explicit formulas and recursive procedures to determine the characteristic polynomials of molecular graphs whose vertices and edges are arbitrarily weighted. Starting from a set of paths and cycles we construct new graphs by joining connected components and adding or inserting edges in a certain way such that the characteristic polynomials of the arising graphs can be recursively obtained. A full description of the class of molecular graphs arising this way is given.

Received: December 20, 2003

AMS Subject Classification: 92E10, 05C50

Key Words and Phrases: molecular graph, weighted graph, characteristic polynomial, LCAO method

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 12
Issue: 1