Super Edge-Magic Labeling of k-Uniform Hypergraphs

Abstract

In this thesis, we generalize the concept of super edge-magic labeling in graph to the super edge-magic labeling in hypergraph. A hypergraph H = (V, E) is super edge-magic if there is a bijection ʄ : Vᴗ E→{1,2,3,…, |+ |} satisfying (i) there exists a constant Ʌ such that for all Σ ʄ(v)+ ʄ€ + Ʌ and (ii) ʄ(v) = {1,2,3,… |} . A necessary condition for a hypergraph being super edge-magic is proved. In particular, the complete -uniform hypergraph is super edge-magic if and only if kϵ{0,1} or nϵ{k,k+1}, the -uniform hyperpath(mp(k)n) is always super edge-magic, and the -uniform hypercycle(mC(k)n) is super edge-magic if and only if is odd or k≠2m.