Graphs with Given Degree Sequence and Maximal Spectral Radius

Graphs with Given Degree Sequence and Maximal Spectral Radius

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 spec...

Graphs with a Given Degree Sequence

The level set G(n, m) comprises all unlabelled simple graphs of order n and size m, and is partitioned into similarity classes, comprising all graphs with the same degree sequence. When graphs are ordered lexicographically by their signature, a unique numerical list of structural descriptors, the similarity classes of G(n, m) occur in contiguous blocks; the first graph in each similarity class ...

Random graphs with a given degree sequence

Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have graph limits in the sense of Lovász and Szegedy with identifiable limits. This allows simple determination of other features such as the number of triangles. ...

Trees with given maximum degree minimizing the spectral radius

The spectral radius of a graph is the largest eigenvalue of the adjacency matrix of the graph. Let T (n,∆, l) be the tree which minimizes the spectral radius of all trees of order n with exactly l vertices of maximum degree ∆. In this paper, T (n,∆, l) is determined for ∆ = 3, and for l ≤ 3 and n large enough. It is proven that for sufficiently large n, T (n, 3, l) is a caterpillar with (almost...

The signless Laplacian spectral radius of graphs with given degree sequences