Triangle-degree and triangle-distinct graphs

Publication Date

1-1-2024

Document Type

Article

Publication Title

Discrete Mathematics

Volume

347

Issue

1

DOI

10.1016/j.disc.2023.113695

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.

Funding Number

1500662

Funding Sponsor

Division of Mathematical Sciences

Keywords

Degree, Triangle-degree, Triangle-distinct graph

Department

Mathematics and Statistics

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