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Spectral polynomials of systems with general interactions
Author(s) -
Balasubramanian K.,
Randíc M.
Publication year - 1985
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560280406
Subject(s) - simple (philosophy) , combinatorics , indifference graph , variety (cybernetics) , mathematics , chordal graph , pruning , graph , philosophy , statistics , epistemology , agronomy , biology
General structures represented by graphs with unequal interactions (weighted edges) are considered and their characteristic polynomials (spectral polynomials) are obtained. It is shown that the procedure based on pruning terminal vertices previously developed by one of the present authors (K.B., Ref. 1) can be generalized to more common graphs in which nonuniform interactions (unequal couplings) occur. Special cases of the present approach are Möbius graphs, signed graphs, directed graphs, multigraphs, and pseudographs (i.e., graphs with multiple connections and graphs with loops, respectively). Weighted graphs (with general weights) are applicable to a variety of chemical problems such as problems of chemical kinetics, analysis of NMR spectra, the study of simple molecular orbitals, and molecular vibrations.