The -centipede
graph,
-centipede
tree,
-comb
graph (Seoud and Youssef 2017), or simply "
-centipede," is the tree on
nodes obtained by joining the bottoms of
copies of the path graph
laid in a row with edges. It is therefore
isomorphic to the
-firecracker graph, with special cases summarized
in the table below.
| graph | |
| 1 | path graph |
| 2 | path graph |
| 3 | E graph |
The rank polynomial of the centipede is given by