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Kayak Paddle Graph

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A kayak paddle graph KP(k,m,l) is the graph obtained by joining cycle graphs C_k and C_m by a path of length l (Gallian 2018).

KP(3,3,1) 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. k=0 (mod 4), m=0,3 (mod 4),

2. k=m=2 (mod 4) for k>=3,

3. k=1 (mod 4), m=3 (mod 4)

(Litersky 2011, Gallian 2018).

See also

Barbell Graph, Cycle Graph, Lollipop Graph, Pan Graph, Tadpole Graph

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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.

Cite this as:

Weisstein, Eric W. "Kayak Paddle Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KayakPaddleGraph.html

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