The term "sun graph" has several differing definitions. 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), Anitha and Lekshmi (2008), and the American Institute of Mathematics 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
.