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Factoring the characteristic polynomial
Author(s) -
Randić M.,
Baker B.,
Kleiner A. F.
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.560280812
Subject(s) - pruning , generalization , mathematics , combinatorics , tree (set theory) , extension (predicate logic) , polynomial , matrix (chemical analysis) , discrete mathematics , computer science , materials science , botany , mathematical analysis , composite material , biology , programming language
We outline an approach, named “ultimate pruning,” for obtaining factors of the characteristic polynomial of trees. The approach is an extension of the pruning method of Balasubramanian in which the size of the determinant ( A‐xI ) is gradually decreased by modifying the entries in the adjacent matrix A for element having terminal bonds. The “ultimate prunings” bypass gradual pruning and starts immediately with a 2 × 2 determinant for a tree, as illustrated on numerous trees having n = 10 and less vertices. Possible application to larger graphs is indicated, few large graphs are considered and some generalization discussed.