  Bootstrap Percolation is a process defined on a graph which begins with an
initial set of infected vertices. In each subsequent round, an uninfected
vertex becomes infected if it is adjacent to at least $r$ previously infected
vertices. If an initially infected set of vertices, $A_0$, begins a process in
which every vertex of the graph eventually becomes infected, then we say that
$A_0$ percolates. In this paper we investigate bootstrap percolation as it
relates to graph distance and connectivity. We find a sufficient condition for
the existence of cardinality 2 percolating sets in diameter 2 graphs when $r =
2$. We also investigate connections between connectivity and bootstrap
percolation and lower and upper bounds on the number of rounds to percolation
in terms of invariants related to graph distance.
