A graph G = (V, E) is weighted-k-antimagic if for each w : V -> R, there is an injective function f : E -> {1,...,vertical bar E vertical bar + k} such that the following sums are all distinct: for each vertex u, Sigma(v:uv ...

A connected graph G=(V,E) with m edges is called universal antimagic if for each set B of m positive integers there is an bijective function f:E→B such that the function f˜:V→N defined at each vertex v as the sum of all ...

Hartsfield and Ringel in 1990 conjectured that any connected graph with q >= 2 edges has an edge labeling f with labels in the set {1,..., q}, such that for every two distinct vertices u and v, f(u) not equal= f(v), where ...