Character degree graphs constitute a powerful tool in the study of finite groups, encapsulating the interplay between group representation theory and graph theory. These graphs are constructed by ...

Let d₁ ≥ d₂ ≥ ··· ≥ dn be the degree sequence of a graph G of order n and μ₁ ≥ μ₂ ≥ ··· ≥ μn = 0 be the Laplacian eigenvalues of G. In this paper, we propose a new conjecture that for any graph G ...

A uniformly random graph on n vertices with a fixed degree sequence, obeying a γ subpower law, is studied. It is shown that, for γ > 3, in a subcritical phase with ...