Self-complementary graph: Difference between revisions

Revision as of 23:10, 7 May 2013

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==Examples==

TheEvery [[Paley graph]] is self-complementary.<ref name="sachs"/> For example, the 3&nbsp;&times;&nbsp;3 [[gridrook's graph]] (the Paley graph of order nine) is self-complementary, by a symmetry that keeps the center vertex in place but exchanges the roles of the four side midpoints and four corners of the grid.<ref>{{citation

| last = Shpectorov | first = S.

| doi = 10.1016/S0012-365X(98)0007X-1

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| title = Complementary ''l''₁-graphs

| volume = 192

Every | [[Paleyyear graph]]= is self-complementary1998}}.</ref name="sachs"/> All [[strongly regular graph|strongly regular]] self-complementary graphs with fewer than 37 vertices are Paley graphs; however, there are strongly regular graphs on 37, 41, and 49 vertices that are not Paley graphs.<ref>{{citation

| year = 1998}}.</ref>

Every [[Paley graph]] is self-complementary.<ref name="sachs"/> All [[strongly regular graph|strongly regular]] self-complementary graphs with fewer than 37 vertices are Paley graphs; however, there are strongly regular graphs on 37, 41, and 49 vertices that are not Paley graphs.<ref>{{citation

| last = Rosenberg | first = I. G.

| contribution = Regular and strongly regular selfcomplementary graphs