Higher Diameters of Random and Cayley Graphs

We study the paper by Erskine and Tuite and generalise some results to higher diameters of either random or large Cayley graphs. When working with random digraphs, where the probability of an edge does not depend on the graph order, we show that for fixed s and t the diameter d(s,t) is almost surely at most 2 as n goes to infinity. Analogs for random Cayley graphs are also explored.