Editing Truncated octahedron (section)

== Truncated octahedral graph ==
{{Infobox graph
 | name = Truncated octahedral graph
 | image = [[File:Truncated octahedral graph2.png|240px]]
 | image_caption = 3-fold symmetric [[Schlegel diagram]]
 | namesake = 
 | vertices = 24
 | edges = 36
 | automorphisms = 48
 | radius = 
 | diameter = 
 | girth = 
 | chromatic_number = 2
 | chromatic_index = 
 | fractional_chromatic_index = 
 | properties = [[Cubic graph|Cubic]], [[hamiltonian graph|Hamiltonian]], [[regular graph|regular]], [[Zero-symmetric graph|zero-symmetric]]
|book thickness=3|queue number=2}}
In the [[mathematics|mathematical]] field of [[graph theory]], a '''truncated octahedral graph''' is the [[1-skeleton|graph of vertices and edges]] of the truncated octahedron. It has 24 [[Vertex (graph theory)|vertices]] and 36 edges, and is a [[cubic graph|cubic]] [[Archimedean graph]].<ref>{{cite book|last1=Read|first1=R. C.|last2=Wilson|first2=R. J.|title=An Atlas of Graphs|publisher=[[Oxford University Press]]|year= 1998|page=269}}</ref> It has [[book thickness]] 3 and [[queue number]] 2.<ref>Wolz, Jessica; ''Engineering Linear Layouts with SAT.'' Master Thesis, University of Tübingen, 2018</ref>

As a [[Hamiltonian graph|Hamiltonian]] [[cubic graph]], it can be represented by [[LCF notation]] in multiple ways: [3, −7, 7, −3]<sup>6</sup>, [5, −11, 11, 7, 5, −5, −7, −11, 11, −5, −7, 7]<sup>2</sup>, and [−11, 5, −3, −7, −9, 3, −5, 5, −3, 9, 7, 3, −5, 11, −3, 7, 5, −7, −9, 9, 7, −5, −7, 3].<ref>{{MathWorld |urlname=TruncatedOctahedralGraph |title=Truncated octahedral graph}}</ref>

[[File:Truncated octahedral Hamiltonicity.svg|600px|thumb|left|Three different Hamiltonian cycles described by the three different [[LCF notation]]s for the truncated octahedral graph]]

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