selfcomplementarity

Self-complementarity is a property in which an object is equivalent to its complement under a specified symmetry or operation. In mathematics and computer science, this often means that the object is isomorphic to its complement, while in biology it typically refers to nucleic acid sequences that read as their reverse complements.

In graph theory, a self-complementary graph on n vertices is one that is isomorphic to its complement. Such graphs can exist only when n is congruent to 0 or 1 modulo 4, and they have exactly n(n−1)/4 edges. The concept commonly relies on a permutation of the vertices that maps adjacency to non-adjacency, effectively turning the graph into its complement. Classic examples include the 4-vertex path P4 and the 5-vertex cycle C5. Self-complementary graphs are studied in relation to graph labeling, symmetry, and Ramsey-type problems.

In molecular biology and biochemistry, a sequence is described as self-complementary if its reverse complement is identical to the sequence itself. For DNA, this means the sequence equals its reverse-complement sequence, allowing the strand to fold back on itself and form structures such as hairpins. Self-complementary sequences are relevant in the design of oligonucleotides, probes, and certain RNA secondary structures, where internal base pairing influences stability and function.

The term can also appear in chemistry and materials science to describe molecules capable of forming complementary interactions within the same molecule or between identical units. Overall, self-complementarity denotes a symmetry between an object and its defined complement, with distinct implications across disciplines.