Graph Complement

The complement of a graph , sometimes called the edge-complement (Gross and Yellen 2006, p. 86), is the graph , sometimes denoted  or  (e.g., Clark and Entringer 1983), with the same vertex set but whose edge set consists of the edges not present in  (i.e., the complement of the edge set of  with respect to all possible edges on the vertex set of ). The graph sum  on a -node graph  is therefore the complete graph , as illustrated above.

A graph complement can be computed in the Wolfram Language by the command GraphComplement[g].

REFERENCES

Clark, L. and Entringer, R. "Smallest Maximally Nonhamiltonian Graphs." Periodica Math. Hungarica 14, 57-68, 1983.

Gross, J. T. and Yellen, J. Graph Theory and Its Applications, 2nd ed. Boca Raton, FL: CRC Press, 2006.

Skiena, S. "The Complement of a Graph." §3.2.3 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, p. 93, 1990.