Further Results on Ph-supermagic Trees

Abstract

Let $G$ be a simple, finite, and undirected graph. An $H$-supermagic labeling is a bijective map $f : V(G) \cup E(G) \to \{1,2,\cdots,|V(G)|+|E(G)|\}$ in which $f(V) = \{1,2,\cdots,|V(G)|\}$ and there exists an integer $m$ such that $w(H') = \sum_{v  \in V(H')} f(v) + \sum_{e \in E(H')} f(e) = m$, for every subgraph $H' \cong H$ in $G$. In this paper, we determine some classes of trees which have $P_h$-supermagic labeling.