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Sun Graph


SunGraph

There are several differing definitions of the sun graph. ISGCI defines a (complete) n-sun graph as a graph on 2n nodes (sometimes also known as a trampoline graph; Brandstädt et al. 1987, p. 112) consisting of a central complete graph K_n with an outer ring of n 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 "n-sun" graph to instead refer to the graph on 2n vertices obtained by attaching n pendant edges to a cycle graph C_n. These graphs are referred to as "sunlet graphs" by ISGCI. The 3-sunlet graph C_3 circledot K_1 is also known as the net graph.

The sun graphs are pancyclic and uniquely Hamiltonian.

The bipartite double graph of the sun graph S_n for n odd is S_(2n).


See also

Hajós Graph, Rising Sun Graph, Sierpiński Gasket Graph, Sunlet 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.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.

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Sun Graph

Cite this as:

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

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