  A graph with $v$ vertices is $(r)$-pancyclic if it contains precisely $r$
cycles of every length from 3 to $v$. A bipartite graph with even number of
vertices $v$ is said to be $(r)$-bipancyclic if it contains precisely $r$
cycles of each even length from 4 to $v$. A bipartite graph with odd number of
vertices $v$ and minimum degree at least 2 is said to be oddly
$(r)$-bipancyclic if it contains precisely $r$ cycles of each even length from
4 to $v-1$. In this paper, using computer search, we classify all
$(r)$-pancyclic and $(r)$-bipancyclic graphs with $v$ vertices and at most
$v+5$ edges. We also classify all oddly $(r)$-bipancyclic graphs with $v$
vertices and at most $v+4$ edges.
