There are several differing definitions of the sun graph. ISGCI defines a (complete) -sun graph as a graph on nodes (sometimes also known as a trampoline graph; Brandstädt
et al. 1987, p. 112) consisting of a central complete
graph
with an outer ring of
vertices, each of which is joined to both endpoints of the closest outer edge of
the central core.
Wallis (2000) and Anitha and Lekshmi (2008) use the term "-sun" graph to instead refer to the graph on vertices obtained by attaching pendant edges to a cycle graph. These graphs are referred to as "sunlet graphs" by ISGCI. The 3-sunlet graph is also known as the
net graph.
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.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.