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arXiv · 1304.1345

Diameter preserving surjections in the geometry of matrices

Wen-ling Huang·Hans Havlicek
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Abstract

We consider a class of graphs subject to certain restrictions, including the finiteness of diameters. Any surjective mapping $\phi:\Gamma\to\Gamma'$ between graphs from this class is shown to be an isomorphism provided that the following holds: Any two points of $\Gamma$ are at a distance equal to the diameter of $\Gamma$ if, and only if, their images are at a distance equal to the diameter of $\Gamma'$. This result is then applied to the graphs arising from the adjacency relations of spaces of rectangular matrices, spaces of Hermitian matrices, and Grassmann spaces (projective spaces of rectangular matrices).

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BibTeXRIS

Wen-ling Huang, Hans Havlicek. 2013-04-04. Diameter preserving surjections in the geometry of matrices. https://doi.org/10.1016/j.laa.2008.02.037

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