A kayak paddle graph is the graph obtained by joining cycle graphs and by a path of length (Gallian 2018). A number of kayak paddle graphs are illustrated above.
is isomorphic to the 3-barbell graph.
Kayak paddle graphs are planar, cactus, unit-distance and matchstick graphs. They are also bridged and traceable and have arboricity of 2.
Litersky (2011) proved that kayak paddle graphs are graceful when:
1. , ,
2. (mod 4) for ,
3. ,
(Litersky 2011, Gallian 2018).