A coloring g: E(G) →C of the edge-set of a graph G into a color-set C is called vertex-distinguishing if g(St(u)) ≠g(St(v)) for any two stars. Let c(G) be the minimal number of colors necessary for such a coloring. For k-regular graphs G we clearly have c(G) ≥ C1n1/k, where n is the order of G. We prove c(G) ≤ C2n1/k, and for k = 2, c(G)≤ 9/√2 √n+C.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics