If every edge in the graph G is also an edge of a subgraph of G isomorphic to a given graph H we say that the graph G admits an H-covering. Let G be a graph admitting an H-covering and let H1, H2, … , Ht be all subgraphs in G isomorphic to H. The edge H-irregularity strength of a graph G is the smallest integer k for which one can find a mapping ϕ : E(G) → {1, 2, … , k} such that ∑e∈E(Hi)ϕ(e) ≠ ∑e∈(Hj)ϕ(e) for every 1 ≤ i