On C4C4-supermagic labelings of the Cartesian product of paths and graphs

A graph GG admits an HH-covering if every edge in E(G)E(G) belongs to a subgraph of GG isomorphic to HH. Suppose GG admits an HH-covering. A bijection ff from V(G)∪E(G)V(G)∪E(G) to {1,2,…,|V(G)|+|E(G)|}{1,2,…,|V(G)|+|E(G)|} is called an HH-magic labeling of GG if ∑v∈V(H′)f(v)+∑e∈E(H′)f(e)∑v∈V(H′)f(v)+∑e∈E(H′)f(e) is constant for every subgraph H′H′ of GG isomorphic to HH. An HH-magic labeling ff of GG is called an HH-supermagic labeling of GG if f(V(G))={1,2,…,|V(G)|}f(V(G))={1,2,…,|V(G)|}. In this paper, we investigate C4C4-supermagic labelings of the Cartesian product of paths and graphs.