Self-Complementary Graphs
Self-complementary graphs are isomorphic to their complements and exhibit unique properties. They are always connected and traceable, with specific conditions regarding their edges and diameter. The enumeration of these graphs can be derived from Pólya's enumeration theorem.
- ▪A self-complementary graph is isomorphic to its graph complement.
- ▪Every self-complementary graph is connected and traceable.
- ▪Self-complementary graphs must have exactly half the total possible number of edges.
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TOPICS Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index New in MathWorld Discrete Mathematics Graph Theory Simple Graphs Connected Graphs Discrete Mathematics Graph Theory Simple Graphs Self-Complementary Graphs Discrete Mathematics Graph Theory Simple Graphs Traceable Graphs History and Terminology Database Collections Integer Sequence Databases Online Encyclopedia of Integer Sequences More...Less... Self-Complementary Graph Download Wolfram Notebook A self-complementary graph is a graph which is isomorphic to its graph complement. The numbers of simple self-complementary graphs on , 2, ...
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