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Partition technique and molecular graph theory
Author(s) -
Kiang YuanSun
Publication year - 2009
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.560200832
Subject(s) - isospectral , adjacency matrix , partition (number theory) , graph theory , mathematics , adjacency list , series (stratigraphy) , graph , molecular graph , combinatorics , discrete mathematics , pure mathematics , paleontology , biology
By means of the partition technique proposed by Löwdin, the original graphical‐deleting method for calculating the determinant a a of adjacency matrix can be generalized to evaluate the characteristic polynomials of molecular graphs and as colloraries, the results obtained by Heilbronner, Schwenk, Tang, and Kiang are reperformed. Furthermore, for molecular graphs to which certain long‐chain cata‐condensed hydrocarbon series correspond, characteristic polynomials are worked out in closed forms. The condition for building up isospectral graphs and the meaning of isospectral points are discussed. Finally, some current algorithms for a a and Kekulé structures are analyzed in a unified way.