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arXiv · 2308.10978

Triangle-degree and triangle-distinct graphs

Zhanar Berikkyzy·Beth Bjorkman·Heather Smith Blake·Sogol Jahanbekam·Lauren Keough·Kevin Moss·Danny Rorabaugh·Songling Shan
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Abstract

Let $G$ be a simple graph and $v$ be a vertex of $G$. The triangle-degree of $v$ in $G$ is the number of triangles that contain $v$. 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.

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Zhanar Berikkyzy, Beth Bjorkman, Heather Smith Blake, Sogol Jahanbekam, Lauren Keough, Kevin Moss, Danny Rorabaugh, Songling Shan. 2023-08-30. Triangle-degree and triangle-distinct graphs. https://arxiv.org/abs/2308.10978

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