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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.
0
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…
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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…
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