• Corpus ID: 235390411

Minimal Regular graphs with every edge in a triangle

  title={Minimal Regular graphs with every edge in a triangle},
  author={James Preen},
  • J. Preen
  • Published 10 June 2021
  • Mathematics
Considering regular graphs with every edge in a triangle we prove lower bounds for the number of triangles in such graphs. For r-regular graphs with r ≤ 5 we exhibit families of graphs with exactly that number of triangles and then classify all such graphs using line graphs and even cycle decompositions. Examples of ways to create such r-regular graphs with r ≥ 6 are also given. In the 5-regular case, these minimal graphs are proven to be the only regular graphs with every edge in a triangle… 

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