Some Cycle-Supermagic Graphs

Abstract

A simple graph $G=(V,E)$ admits an $H$-covering if every edge in $E$ belongs to a subgraph of $G$ isomorphic to $H$. $G$ is $H$-magic if there is a total labeling $f:V\cup E\rightarrow\{1,2,3,\cdots,|V|+|E|\}$ such that for each subgraph $H'=(V',E')$ of $G$ isomorphic to $H$, $ \underset{v \in V_1}\sum f(v)+\underset{e \in E_1}\sum f(e)=s$ is constant. When $f(V)=\{1,2, \cdots,|V|\}$, then $G$ is said to be $H$-supermagic. In this paper, we show that $P_{m,n}$ and the splitting graph of a cycle $C_{n}$ are cycle-supermagic.