Authors: Stevanović, Dragan 
Ghebleh, Mohammad
Caporossi, Gilles
Vijayakumar, Ambat
Stevanović, Sanja 
Affiliations: Computer Science 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On regular triangle-distinct graphs
Journal: Computational and Applied Mathematics
Volume: 43
Issue: 6
First page: 336
Issue Date: 1-Sep-2024
Rank: ~M21
ISSN: 2238-3603
DOI: 10.1007/s40314-024-02854-9
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 first showcase the examples of regular, triangle-distinct graphs, and then show that for every natural number k there exists a family of 2k regular triangle-distinct graphs, all having the same order and size.
Keywords: 05C07 | 05C99 | Asymmetric graph | Number of triangles | Regular graph
Publisher: Springer Link

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