Super edge-magic labeling of m-node k-uniform hyperpaths and m-node k-uniform hypercycles

Abstract

We generalize the notion of the super edge-magic labeling of graphs to the notion of the super edge-magic labeling of hypergraphs. For a hypergraph H with a finite vertex set V and a hyperedge set E, a bijective function f:V∪E→{1,2,3,…,|V|+|E|} is called a super edge-magic labeling if it satisfies (i) there exists a magic constant Λ such that f(e)+∑v∈ef(v)=Λ for all e∈E and (ii) f(V)={1,2,3,…,|V|}. A hypergraph admitting a super edge-magic labeling is said to be super edge-magic. In this paper, we show the equivalent form of this labeling, i.e, a hypergraph H is super edge-magic if and only if there exists a bijective function f:V→{1,2,3,…,|V|} such that {∑v∈ef(v)|e∈E} is the set of |E| consecutive integers. Finally, we define two classes of hypergraphs, namely m-node k-uniform hyperpaths and m-node k-uniform hypercycles which are denoted by mPn(k) and mCn(k), respectively. We show that under some conditions the hypergraphs mPn(k) and mCn(k) are super edge-magic.

Keywords

• Super edge magic labeling
• Hyper graph
• Hypergraph labeling