Edge Cover in a Hypergraph

Abstract

In this paper we introduce a new concept called an edge cover of a hypergraph. We characterize a minimal edge cover in hypergraph. We proved that if G is a hypergraph with minimum edge degree $\geq$ 2 then the complement of a minimal edge cover is an edge h-dominating set of G. We also proved a necessary \& sufficient condition under which the edge covering number of a hypergraph decreases when a vertex v is removed from the hypergraph. We also prove corresponding results for the partial sub hypergraph obtained by removing a vertex from the hypergraph.