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