Triangle-degree and triangle-distinct graphs
Combinatorics
2023-08-31 v2
Abstract
Let be a simple graph and be a vertex of . The triangle-degree of in is the number of triangles that contain . 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}
}