Abstract
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 H-1, H-2, ... , H-t 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 phi : E(G) -> {1, 2, ... , k} such that Sigma(e is an element of E(Hi))phi(e) not equal Sigma(e is an element of(Hj))phi(e) for every 1 <= i < j <= t. In this paper, we determine the exact values of ehs(G, C-4) for a grid graph and a generalized prism.