Exponential graphs are graphs in the form \(y = k^x\). These graphs increase rapidly in the \(y\) direction and will never fall below the \(x\)-axis.

We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain exact estimates ...

A PHASE relation familiar to students of applied mathematics exists between a simple harmonic oscillation and its derivative. Similar relations exist between exponential functions and their ...