Folkman graph

Folkman graph
Drawing following Folkman (1967), Figure 1
Named afterJon Folkman
Vertices20
Edges40
Radius3
Diameter4
Girth4
Automorphisms5! · 25 = 3840
Chromatic number2
Chromatic index4
Genus3
Book thickness3
Queue number2
Properties
Table of graphs and parameters

In the mathematical field of graph theory, the Folkman graph is a 4-regular graph with 20 vertices and 40 edges. It is a regular bipartite graph with symmetries taking every edge to every other edge, but the two sides of its bipartition are not symmetric with each other, making it the smallest possible semi-symmetric graph.[1] It is named after Jon Folkman, who constructed it for this property in 1967.[2]

The Folkman graph can be constructed either using modular arithmetic or as the subdivided double of the five-vertex complete graph. Beyond the investigation of its symmetry, it has also been investigated as a counterexample for certain questions of graph embedding.

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  2. ^ Cite error: The named reference folkman was invoked but never defined (see the help page).