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.
The sun graphs are pancyclic and uniquely Hamiltonian.
The bipartite double graph of the sun graph for
odd is
.