For a graph G and a subset A of its vertices denote by Bdry(A) the set of vertices of the complement that are at distance 1 from A. Furthermore, denote by Ball(A) the ball around A, i.e. the union of A and Bdry(A).
This tool displays two graphs G and H defined by their ball-sequences as well their cartesian product. The i-th element of such sequence is the minimum size of the ball around a set of size i, for i=1, 2, ... , |G|. We assume that the graphs are connected. Hence, the ball-sequences are not decreasing, and their i-th entry is at least min(i+1, |G|), for i=1, 2, ... , |G|.
The ball-sequence does not specify the graph uniquely. Moreover, not any ball-sequence satisfying the above properties is realized by some graph. However, any such sequence is realized by an oriented graph. In this case the boundary is defined as the set of vertices that can be reached from A by outgoing edges. The oriented graph is obtained by connecting the vertex i with the vertices {j < i : |Ball(j)| > i-1}.
Enter the ball-sequences into the corresponding input fields of the tool separate the entries by spaces. The corresponding graphs will be displayed. The edges connecting vertices within a level are omitted. The orientation of edges is not shown. This tool is currently intended for drawing non-oriented graphs. By clicking the "Show GxH" button, the product of two graphs will be displayed in a separate tab.