Elegant vertex labelings with prime numbers

Thierry Gensane (1)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

We consider graph labelings with an assignment of odd prime numbers to the vertices. Similarly to graceful graphs, a labeling is said to be elegant if the absolute differences between the labels of adjacent vertices describe exactly the first even numbers. The labels of an elegant tree with n vertices are the first n odd prime numbers and we want that the resulting edge labels are exactly the first even numbers up to 2n − 2. We conjecture that each path is elegant and we give the algorithm with which we got elegant paths of n primes for all n up to n = 3500.

Domaines: Mathématiques [math]

Thierry Gensane. Elegant vertex labelings with prime numbers. 2019. ⟨hal-04546524⟩