Sunlet Graph

The -sunlet graph is the graph on  vertices obtained by attaching  pendant edges to a cycle graph  (ISGCI), i.e., the coronas  (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 .

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 "-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  in the I graph  is loosened, the -sunlet graph corresponds to .

REFERENCES

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." Elec. J. Combin. DS6. Dec. 21, 2018.

 https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS6.ISGCI: Information System on Graph Class Inclusions v2.0. "List of Small Graphs." http://www.graphclasses.org/smallgraphs.html.

Wallis, W. D. Magic Graphs. Boston, MA: Birkhäuser, 2000.