Tuerker Biyikoglu, Josef Leydold
Published 2006-05-11, updated 2008-10-07Version 3
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.
Comments: 12 pages, 4 figures; revised version. Important change: Theorem 3 (formely Theorem 7) now states (and correctly proofs) the majorization result only for "degree sequences of trees" (instead for general connected graphs). Bo Zhou from the South China Normal University in Guangzhou, P.R. China, has found a counter-example to the stronger result
Journal: Electr. J. Comb. 15(1), R119, 2008
Algebraic Connectivity and Degree Sequences of Trees
Trees with given degree sequences that have minimal subtrees
Largest Laplacian Eigenvalue and Degree Sequences of Trees
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