A Note on d-Biclique Covers

A d-biclique cover of a graph G is a collection of bicliques of G such that each edge of G is in at least d of the bicliques. The number of bicliques in a minimum d-biclique cover of G is called the d-biclique covering number of G and is denoted by ${bc}_d(G)$. In this paper, we present an upper bound for the d- biclique covering number of the lexicographic product of graphs. Also, we introduce some bounds of this parameter for some graph constructions and obtain the exact value of the d-biclique covering number of some graphs.