The metric dimension is a key invariant in graph theory that encapsulates the minimal number of reference points, or “resolving sets”, required to uniquely determine the position of each vertex within ...

This is a preview. Log in through your library . Abstract In a random graph, counts for the number of vertices with given degrees will typically be dependent. We show via a multivariate normal and a ...

In math, as in life, small choices can have big consequences. This is especially true in graph theory, a field that studies networks of objects and the connections between them. Here’s a little puzzle ...

On independent random points U1,⋯ ,Un distributed uniformly on [0,1]d, a random graph Gn(x) is constructed in which two distinct such points are joined by an edge if the l∞-distance between them is at ...