Phased graphs and graph energies

We define a phased graph G to yield an adjacency matrix A ( G ) having general magnitude-1 values in the same locations as the usual unphased case, but subject to the restriction that A be Hermitian. Some characteristics of such phased graphs and their eigenspectra are contemplated and to some exten...

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Bibliographic Details
Published inJournal of mathematical chemistry Vol. 49; no. 7; pp. 1238 - 1244
Main Authors Klein, Douglas J., Rosenfeld, Vladimir R.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.08.2011
Springer
Subjects
Chemistry
Chemistry and Materials Science
Exact sciences and technology
General and physical chemistry
Math. Applications in Chemistry
Mathematics
Nonlinear algebraic and transcendental equations
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Original Paper
Physical Chemistry
Sciences and techniques of general use
Theoretical and Computational Chemistry
Theory of reactions, general kinetics. Catalysis. Nomenclature, chemical documentation, computer chemistry
Phased graph
Eigenvalue
Total energy
Phases
Eigenspectrum
Eigenvector
Mathematical chemistry
Graph
Adjacency matrix
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ISSN0259-9791
1572-8897
DOI10.1007/s10910-011-9814-7

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Summary:We define a phased graph G to yield an adjacency matrix A ( G ) having general magnitude-1 values in the same locations as the usual unphased case, but subject to the restriction that A be Hermitian. Some characteristics of such phased graphs and their eigenspectra are contemplated and to some extent described. Different graph energies are defined as suitable sums over adjacency-matrix eigenvalues, with “occupation-number” coefficients .
ISSN:0259-9791
1572-8897
DOI:10.1007/s10910-011-9814-7