On H-antimagic coverings for m-shadow and closed m-shadow of connected graphs

An $$ -H-antimagic total labeling of a simple graph G admitting an H-covering is a bijection $$ such that for all subgraphs $$ of G isomorphic to H, the set of $$ -weights given by $$ forms an arithmetic sequence $$ where $$ , $$ are two fixed integers and t is the number of all subgraphs of G isomorphic to H. Moreover, such a labeling φ is called super if the smallest possible labels appear on the vertices. A (super) $$ -H-antimagic graph is a graph that admits a (super) $$ -H-antimagic total labeling. In this paper the existence of super $$ -H-antimagic total labelings for the m-shadow and the closed m-shadow of a connected G for several values of d is proved.