Abstract
We consider a class of graphs which satisfies a set of certain conditions. Let G , G ′ be such graphs with set of vertices P , P ′ . Let 1 ⩽ k < diam G ) be a positive integer, and let φ : P → P ′ be a surjection satisfying d ( x , y ) ⩽ k ⇔ d ( x φ , y φ ) ⩽ k for all x , y ∈ P . We show that φ is an isomorphism between G and G ′ . This result is applied to the graphs arising from the adjacency relations of the spaces of rectangular matrices, symmetric matrices, Hermitian matrices, alternate matrices, and Grassmann spaces.
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