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Undergraduate
By
Shiva Kintali
on Oct. 3, 2013 | Updated Jan. 4, 2018
Self-complementary planar graphs
Prove that the complement of a simple planar graph with at least \(11\) vertices is nonplanar. Construct two self-complementary simple planar graphs with \(8\) vertices.
Mathematics
Graph Theory
graph complement
planar graphs
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Undergraduate
By
Shiva Kintali
on May 19, 2013 | Updated Dec. 6, 2017
Self-complementary graphs
Let \(G\) be a self-complementary graph (i.e., \(G\) is isomorphic to its complement) on \(n\) vertices. Prove that \(n \equiv 0\ (mod\ 4)\) or \(n \equiv -1\ (mod\ 4)\). Prove that \(G\) has a cut…
Mathematics
Graph Theory
graph complement
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Undergraduate
By
Shiva Kintali
on Sept. 27, 2013 | Updated Jan. 4, 2018
Graph complement
Let \(G\) be an undirected graph without self-loops and multi-edges. The complement of graph \(G\) is a graph \(\overline{G}\) on the same vertices such that two vertices of \(\overline{G}\) are adjac…
Mathematics
Graph Theory
connectivity
graph complement
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