The graph excision 
of a tree 
that is a subgraph of a cubic
graph 
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.
