On Super Edge-Magic $n$-Stars

Abstract

A $(p,q)$ graph $G$ is $totaledge-magic$ if there exists a bijection $\text{f}:\text{V}\cup \text{E}\to \{1,2,\dots ,\text{p+q}\}$ such that $\mathrm{\forall }\text{e}=\text{(u,v)}\in \text{E}$, f(u) + f(e) + f(v) = constant. A total edge-magic graph is a $superedge-magicgraph$ if $\text{f(V(G))}=\{1,2,\dots ,\text{p}\}$. For $\text{n}\ge 2$, let ${\text{a}}_1,{\text{a}}_2,{\text{a}}_3,\dots ,{\text{a}}_{\text{n}}$ be a sequence of increasing non-negative integers. A n-star $S({\text{a}}_1,{\text{a}}_2,{\text{a}}_3,\dots ,{\text{a}}_{\text{n}})$ is a disjoint union of n stars $\text{St}({\text{a}}_1),\text{ St}({\text{a}}_2),\dots ,\text{St}({\text{a}}_{\text{n}})$. In this paper, we investigate several classes of n-stars that are super edge-magic.