Let a tree be a subgraph of a cubic graph
. The graph excision is the graph resulting from removing the tree,
then merging the edges. For example, if in the Tutte
8-cage (left figure) the tree formed by the 6 interior points (middle figure)
is excised, the McGee graph (right figure) results.
Similarly, excising the Heawood graph gives the
Petersen graph, and excising the generalized
hexagon (i.e., the unique 12-cage graph) gives
the Balaban 11-cage (Biggs 1998).

The reverse of excision is insertion. Both operations are used in the analysis of
cages.

The following table gives some cubic symmetric
graphs with named edge-excised graphs, illustrated above.