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Title

A CONNECTION BETWEEN FRAMES AND GRAPHS

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Abstract

 LET H BE A FINITE DIMENSIONAL HILBERT SPACE AND J BE A FINITE FRAME IN H. WE ASSOCIATE A SIMPLE GRAPH G (J) TO J, WHICH IS CALLED FRAME GRAPH, WHOSE VERTICES ARE THE ELEMENTS OF J AND TWO DISTINCT VERTICESA AND B ARE ADJACENT IF AND ONLY IF <A,B>¹0. WE INVESTIGATE THE INTERPLAY BETWEEN THE FRAME-THEORETIC PROPERTIES OF J AND THE GRAPH-THEORETIC PROPERTIES OF G (J).

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