2019/07/02 by Thierry Gensane, Gensane, Thierry
Computer Science · Engineering · #05C78 #11A41 #11Z99 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1907.01249
openalex publication_date 2019/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.