(H\)-supermagic labelings for firecrackers, banana trees and flowers

A simple graph \(G=(V,E)\) admits an \(H\)-covering if every edge in \(E\) is contained in a subgraph \(H'=(V',E')\) of \(G\) which is isomorphic to \(H\). In this case we say that \(G\) is \(H\)-supermagic if there is a bijection \(f:V\cup E\to\{1,\ldots\lvert V\rvert+\lvert E\rvert\}\) such that \(f(V)=\{1,\ldots,\lvert V\rvert\}\) and \(\sum_{v\in V(H')}f(v)+\sum_{e\in E(H')}f(e)\) is constant over all subgraphs \(H'\) of \(G\) which are isomorphic to \(H\). In this paper, we show that for odd \(n\) and arbitrary \(k\), the firecracker \(F_{k,n}\) is \(F_{2,n}\)-supermagic, the banana tree \(B_{k,n}\) is \(B_{1,n}\)-supermagic and the flower \(F_n\) is \(C_3\)-supermagic.