New families of star-supermagic graphs

Abstract

A simple graph $G$ admits a \textit{$K_{1, n}$-covering} if every
edge in $E(G)$ belongs to a subgraph of $G$ isomorphic to $K_{1, n}$. The
 graph $G$ is $K_{1, n}$-supermagic if there exists  a bijection $f : V(G)
\cup E(G) \rightarrow \{1, 2, 3, \cdots, |V(G) \cup E(G)|\}$ such
that for every subgraph $H'$ of $G$ isomorphic to $K_{1, n}$, $\sum_{v \in
V(H')} f(v) + \sum_{e \in E(H')} f(e)$ is  a constant and $f(V(G)) = \{1, 2, 3, \cdots, |V(G)|\}$. In such a case, $f$ is called a $K_{1, n}$-supermagic labeling of $G$.  In this paper, we give a method how to construct  $K_{1, n}$-supermagic graphs from the old ones.