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![]() In graph theory, you can consider graphs as dimensionless objects. Fine. It is known that some graphs can not be drawn on paper without crossing edges. Fact. Graphs are connected with several kinds of matrices: incidence, Laplace Kirchhoff, adjacency, distance, etc.. Fact. These matrices have eigenvalues. Fact The number of nonzero eigenvalues determines the dimensionality of the graph (at least the mathematical one). Hypothesis. Elements of distance matrices are the number of edges between two vertices. The largest distance in the linear chain x-x-x-x is 3, similarly as the largest distance in cube. Fact Try to use squared distances, 9 for the linear chain, 3 for the cube. in this case, the number of nonzero eigenvalues is determined by the shape of the arranged objects, not by their number. Fact Physical, chemical and biological properties of molecules depend on eigenvalues of their matrices (or their sums). Fact It is simpler to consider molecules as multidimensional objects embedded into 3 dimensions than to explain observed facts by other theories. kunzmilan |
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