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{\bf T\"urker B{\i}y{\i}ko\u{g}lu and Josef Leydold}
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{\bf Graphs with Given Degree Sequence and Maximal Spectral Radius}
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We describe the structure of those graphs that have largest spectral
radius in the class of all connected graphs with a given degree
sequence. We show that in such a graph the degree sequence is
non-increasing with respect to an ordering of the vertices induced by
breadth-first search.  For trees the resulting structure is uniquely
determined up to isomorphism. We also show that the largest spectral
radius in such classes of trees is strictly monotone with respect to
majorization.



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