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Searching for regular, triangle-distinct graphs

Dragan Stevanović, Mohammad Ghebleh, Gilles Caporossi, Ambat Vijayakumar, Sanja Stevanović

Abstract

The triangle-degree of a vertex v of a simple graph G is the number of triangles in G that contain v. A simple graph is triangle-distinct if all its vertices have distinct triangle-degrees. Berikkyzy et al. [Discrete Math. 347 (2024) 113695] recently asked whether there exists a regular graph that is triangle-distinct. Here we showcase the examples of regular, triangle-distinct graphs with orders between 21 and 27, and report on the methodology used to find them.

Searching for regular, triangle-distinct graphs

Abstract

The triangle-degree of a vertex v of a simple graph G is the number of triangles in G that contain v. A simple graph is triangle-distinct if all its vertices have distinct triangle-degrees. Berikkyzy et al. [Discrete Math. 347 (2024) 113695] recently asked whether there exists a regular graph that is triangle-distinct. Here we showcase the examples of regular, triangle-distinct graphs with orders between 21 and 27, and report on the methodology used to find them.
Paper Structure (1 section, 13 equations, 1 figure)

This paper contains 1 section, 13 equations, 1 figure.

Table of Contents

  1. Adjacency lists of regular, triangle-distinct graphs

Figures (1)

  • Figure 1: An example of a 10-regular, triangle-distinct graph on 21 vertices.