For every degree sequence of a t-cone tree, unicyclic, or bicyclic graph, the unique general-spectral-radius-maximizing graph is the BFS-type join graph, and strict majorization raises the maximum for c=0,1.
Extremal Graph Theory for Degree Sequences
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abstract
This paper surveys some recent results and progress on the extremal prob- lems in a given set consisting of all simple connected graphs with the same graphic degree sequence. In particular, we study and characterize the extremal graphs having the maximum (or minimum) values of graph invariants such as (Laplacian, p-Laplacian, signless Laplacian) spectral radius, the first Dirichlet eigenvalue, the Wiener index, the Harary index, the number of subtrees and the chromatic number etc, in given sets with the same tree, unicyclic, graphic degree sequences. Moreover, some conjectures are included.
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The general spectral radius and majorization theorem of $t$-cone graphs with given degree sequences
For every degree sequence of a t-cone tree, unicyclic, or bicyclic graph, the unique general-spectral-radius-maximizing graph is the BFS-type join graph, and strict majorization raises the maximum for c=0,1.