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.
Levit, V. E. and Mandrescu, E. "The Independence Polynomial of a Graph--A Survey." In Proceedings of the 1st International
Conference on Algebraic Informatics. Held in Thessaloniki, October 20-23, 2005
(Ed. S. Bozapalidis, A. Kalampakas, and G. Rahonis). Thessaloniki,
Greece: Aristotle Univ., pp. 233-254, 2005.Seoud, M. Z. and
Youssef, M. A. "On Gracefulness of Disconnected Graphs." Unpublished
work. Jan. 2017. http://dx.doi.org/10.13140/RG.2.2.17752.49920.