Structural covariance of graphs |
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Authors: | Oktay Sinanoğlu |
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Institution: | (1) Sterling Chemistry Laboratory, Yale University, 06520 New Haven, CT, USA |
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Abstract: | Algebraic structures including multiple rank tensors, linear and non-linear operators are related to and represented with various types of graphs. Special emphasis is placed on linear operators e.g. on the Hibert space. A different graph represents the same operator depending on the basis frame used, in general non-orthonormal. All such graphs are shown to belong in one equivalence class and are termed structurally covariant. Crucial indices related to eigenvalues but invariant under any basis frame changes including non-orthonormal ones provide one way to characterize each class. A set of rules are given that allow one to find the graphs structurally covarinat with a given one and/or to deduce the class indices directly by simple pictorial manipulations on a graph. Applications in various fields including the quantum theory of molecules and reactions are indicated. |
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Keywords: | Structural covariance transformation of graphs |
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