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An extension of Frost–Musulin and Möbius–Zimmerman diagrams
Author(s) -
Zhou Zhongxiang
Publication year - 1994
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.560510402
Subject(s) - graph , combinatorics , extension (predicate logic) , degenerate energy levels , inversion (geology) , mathematics , discrete mathematics , physics , computer science , quantum mechanics , paleontology , structural basin , biology , programming language
The eigenspectrum of a Möbius graph is a complete inversion of a Hückel graph for odd‐numbered monocycles. For even‐numbered monocycles, the Coulson‐paired levels ( x i , – x i ) in a Hückel graph become the degenerate levels ( x ′ 1 , x ′ 1 ) in a Möbius graph. Here, we present the proof of a general theorem stating that the same eigenspectral relationship is found in a much wider class of graphs. © 1994 John Wiley & Sons, Inc.