On supermagic coverings of fans and ladders

Abstract

A simple graph $G$ admits an $H$-covering if every edge in $E(G)$ belongs to a subgraph of $G$ isomorphic to $H$. The graph $G$ is said to be $H$-magic if there exists a bijection $f:V(G){\cup }^{\text{}}E(G)\to \{1,2,3,\cdots ,|V(G)\cup E(G)\left|\right\}$ such that for every subgraph $H^{\prime }$ of $G$ isomorphic to $H$, ${\displaystyle {\sum }_{v\in V(H^{\prime })}f(v)}+{\displaystyle {\sum }_{e\in E(H^{\prime })}f(e)}$ is constant. Additionally, $G$ is said to be $H$-supermagic if $f(V(G))=\{1,2,3,\cdots ,|V(G)\left|\right\}$. In this paper, we study $H$-supermagic labelings of two classes of connected graph namely fans and ladders.