Resumen
A 3-connected graph is minimally 3-connected if removal of any edge destroys 3-connectivity. We present an algorithm for constructing minimally 3-connected graphs based on the results in (Dawes, JCTB 40, 159-168, 1986) using two operations: adding an edge between non-adjacent vertices and splitting a vertex. To test sets of vertices and edges for 3-compatibility, which depends on the cycles of the graph, we develop a method for obtaining the cycles of ??'
G
'
from the cycles of G, where ??'
G
'
is obtained from G by one of the two operations above. We eliminate isomorphic duplicates using certificates generated by McKay?s isomorphism checker nauty. The algorithm consecutively constructs the non-isomorphic minimally 3-connected graphs with n vertices and m edges from the non-isomorphic minimally 3-connected graphs with ??-1
n
-
1
vertices and ??-2
m
-
2
edges, ??-1
n
-
1
vertices and ??-3
m
-
3
edges, and ??-2
n
-
2
vertices and ??-3
m
-
3
edges.