Abstract
A simple graph G = (V (G), E (G)) admits an H-covering if every edge in E (G) belongs at least to one subgraph of G isomorphic to a given graph H. Then the graph G admitting H-covering admits an H-irregular total k-labeling f : V (G)U E(G) -> {1, 2, ..., k} if for every two different subgraphs H' and H" isomorphic to H there is wtf (H') not equal wtf (H"), where wtf(H) = Sigma(v is an element of V(H)) f(v) + Sigma(v is an element of V(H)) f(e) is the associated H-weight. The minimum k for which the graph G has an H-irregular total k-labeling is called the total H-irregularity strength of the graph G.
In this paper, we obtain the precise value of the total H-irregularity strength of G-amalgamation of graphs.