For a graph G an edge-covering of G is a family of subgraphs H 1 , H 2 , . . . , H t such that each edge of E(G) belongs to at least one of the subgraphs H i , i = 1, 2, . . . , t. In this case we say that G admits an (H 1 , H 2 , . . . , H t )-(edge) covering. An H-covering of graph G is an (H 1 , H 2 , . . . , H t )-(edge) covering in which every subgraph H i is isomorphic to a given graph H.Let G be a graph admitting H-covering. An edge k-labeling α : E(G) → {1, 2, . . . , k} is called an H-irregular edge k-labeling of the graph G if for every two different subgraphs H ′ and H ′′ isomorphic to H their weights 1 Corresponding author.
2Naeem, Siddiqui, Bača, Semaničová-Feňovčíková and Ashraf wt α (H ′ ) and wt α (H ′′ ) are distinct. The weight of a subgraph H under an edge k-labeling α is the sum of labels of edges belonging to H. The edge H-irregularity strength of a graph G, denoted by ehs(G, H), is the smallest integer k such that G has an H-irregular edge k-labeling.In this paper we determine the exact values of ehs(G, H) for prisms, antiprisms, triangular ladders, diagonal ladders, wheels and gear graphs. Moreover the subgraph H is isomorphic to only C 4 , C 3 and K 4 .
