On a Visibility Representation of Graphs

We give a visibility representation of graphs which extends some very well-known representations considered extensively in the literature. Concretely, the vertices are represented by a collection of parallel hyper-rectangles in R^n and the visibility is orthogonal to those hyper-rectangles. With this generalization, we can prove that each graph admits a visibility representation. But, it arises the problem of determining the minimum Euclidean space where such representation is possible. We consider this problem for concrete well-known families of graphs such as planar graphs, complete graphs and complete bipartite graphs