Kayak Paddle Graph

A kayak paddle graph  is the graph obtained by joining cycle graphs  and  by a path of length  (Gallian 2018).

 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).

REFERENCES

Gallian, J. "Dynamic Survey of Graph Labeling." Elec. J. Combin. DS6. Dec. 21, 2018. https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS6.

Litersky, A. "Graceful Kayak Paddles." M.S. Thesis. Duluth, MN: University of Minnesota Duluth, 2011.