HH-supermagic labelings of graphs

A simple graph GG admits an H-covering   if every edge in E(G)E(G) belongs to a subgraph of GG isomorphic to HH. The graph GG is said to be HH-magic   if there exists a bijection f:V(G)∪E(G)→{1,2,3,…,|V(G)∪E(G)|}f:V(G)∪E(G)→{1,2,3,…,|V(G)∪E(G)|} such that for every subgraph H′H′ of GG isomorphic to HH, ∑v∈V(H′)f(v)+∑e∈E(H′)f(e)∑v∈V(H′)f(v)+∑e∈E(H′)f(e) is constant. GG is said to be HH-supermagic   if f(V(G))={1,2,3,…,|V(G)|}f(V(G))={1,2,3,…,|V(G)|}. In this paper, we study cycle-supermagic labelings of chain graphs, fans, triangle ladders, graphs obtained by joining a star K1,nK1,n with one isolated vertex, grids, and books. Also, we study PtPt-(super)magic labelings of cycles.