In this thesis, we study the biclique covering of graphs. A covering of is a family of subgraphs, say ,…,, having the property that each edge of is contained in at least one graph , for some . If all ,, belong to a specified type="#_x0000_t75" If we require all subgraphs in the covering to be edge-disjoint, the covering is also called a decomposition of One of the fundamental topics in graph is to study the edge covering of graphs. Much work has been done on H-covering for various complet e bipartite graphs H-covering is called an biclique covering. The biclique covering number of a graph is the smallest number of bicliques in a biclique covering. The smallest number of bicliques in a biclique decomposition is known as the biclique partition number and is denoted by . Note that hold for any graph G on n vertices, just because stars are bicliques. These measures of graphs were considered by many authors. The type="#_x0000_t75" ; here Kn is a complete graph on n vertices. On the other hand, we have bc ( Kn ) =