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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 ofvertices $v$ 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 ofvertices $v$ and minimum degree at least 2 is said to be oddly$(r)$-bipancyclic if it contains precisely $r$ cycles of each even length from4 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.

$(r)$-Pancyclic, $(r)$-Bipancyclic and Oddly $(r)$-Bipancyclic Graphs