English

The 2-switch-degree of a graph

Combinatorics 2026-03-10 v2

Abstract

In this work, we delve into the study of the 2-switch-degree of a graph GG, which is nothing more than the degree of GG as a vertex of the realization graph G(d)\mathcal{G}(d) associated with the degree sequence dd of GG. We explore the characteristics of active and inactive vertices, the basic properties of the degree, explicit formulas for its computation, and its behavior in specific families of graphs, such as trees and unicyclic graphs.

Keywords

Cite

@article{arxiv.2511.23327,
  title  = {The 2-switch-degree of a graph},
  author = {Victor N. Schvöllner and Adrián Pastine},
  journal= {arXiv preprint arXiv:2511.23327},
  year   = {2026}
}
R2 v1 2026-07-01T07:59:40.833Z