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Net signs of molecular graphs: Dependence of molecular structure
Author(s) -
Gutman Ivan,
Lee ShyiLong,
Luo YeungLong,
Yeh YeongNan
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.560490204
Subject(s) - eigenvalues and eigenvectors , combinatorics , enhanced data rates for gsm evolution , sign (mathematics) , graph , simple (philosophy) , molecular graph , mixed graph , mathematics , chemistry , physics , line graph , computer science , quantum mechanics , voltage graph , philosophy , artificial intelligence , mathematical analysis , epistemology
The concept of internal connectivity associates to each eigenvector of the molecular graph a graph with signed edges. We show that the respective edge signs can be deduced without knowing the graph eigenvectors. The dependence of the edge signs on molecular structure is elucidated. The sign of an edge whose end vertices are ν r and ν s is found to be the result of separate interactions through all paths connecting the vertices ν r and ν s . The analysis of the edge signs is particularly simple in the case of acyclic systems. © 1994 John Wiley & Sons, Inc.