English

Triangle-degree and triangle-distinct graphs

Combinatorics 2023-08-31 v2

Abstract

Let GG be a simple graph and vv be a vertex of GG. The triangle-degree of vv in GG is the number of triangles that contain vv. While every graph has at least two vertices with the same degree, there are graphs in which every vertex has a distinct triangle-degree. In this paper, we construct an infinite family of graphs with this property. We also study the vertex degrees and size of graphs with this property.

Keywords

Cite

@article{arxiv.2308.10978,
  title  = {Triangle-degree and triangle-distinct graphs},
  author = {Zhanar Berikkyzy and Beth Bjorkman and Heather Smith Blake and Sogol Jahanbekam and Lauren Keough and Kevin Moss and Danny Rorabaugh and Songling Shan},
  journal= {arXiv preprint arXiv:2308.10978},
  year   = {2023}
}
R2 v1 2026-06-28T12:00:48.805Z