Triangle-degree and triangle-distinct graphs

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.(c) 2023 Elsevier B.V. All rights reserved.