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Sunlet Graph


SunletGraphs

The n-sunlet graph is the graph on 2n vertices obtained by attaching n pendant edges to a cycle graph C_n (ISGCI), i.e., the coronas C_n circledot K_1 (Frucht 1979). Sunlet graphs have also been called crown graphs (e.g., Gallian 2018), a terminology that conflicts with the use of the term "crown graph" in this work to refer to a rook complement graph K_2 square K_n^_. They are also known as "sun graphs," which conflicts with the use of that term in this work.

Sunlet graphs are trivially unit-distance graphs, as well as matchstick graphs. They are also graceful (Frucht 1979).

Note that Wallis (2000) and Anitha and Lekshmi (2008) use the term "n-sun" graph to refer to sunlet graphs, whereas ISGCI and other authors reserve that term for a different type of graph.

The 3-sunlet graph is also known as the net graph.

If the restriction j,k<n in the I graph I(n,j,k) is loosened, the n-sunlet graph corresponds to I(n,1,n).


See also

Net Graph, Sun Graph

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References

American Institute of Mathematics. "Graph Catalog: Families of Graphs." https://aimath.org/WWN/matrixspectrum/catalog2.html.American Institute of Mathematics. "AIM Minimum Rank Graph Catalog." http://admin.aimath.org/resources/graph-invariants/minimumrankoffamilies/#/super.Anitha, R. and Lekshmi, R. S. "N-Sun Decomposition of Complete, Complete Bipartite and Some Harary Graphs." Int. J. Math. Sci. 2, 33-38, 2008.Brandstädt, A.; Le, V. B.; and Spinrad, J. P. Graph Classes: A Survey. Philadelphia, PA: SIAM, p. 112, 1987.Frucht, R. "Graceful Numbering of Wheels and Related Graphs." Ann. New York Acad. Sci. 319, 219-229, 1979.Gallian, J. "Dynamic Survey of Graph Labeling." Electronic J. Combinatorics, Dynamic Survey DS6, Oct. 30, 2025. https://doi.org/10.37236/27.House of Graphs. Sunlet Graphs. Net Graph, Corona of C4, Corona of C5, Corona of C6, Sunlet Graph 7, Sunlet Graph 8, Sunlet Graph 9, Sunlet Graph 10, and Sunlet Graph 11.ISGCI: Information System on Graph Class Inclusions v2.0. "List of Small Graphs." https://www.graphclasses.org/smallgraphs.html.Wallis, W. D. Magic Graphs. Boston, MA: Birkhäuser, 2000.

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Sunlet Graph

Cite this as:

Weisstein, Eric W. "Sunlet Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SunletGraph.html

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