Editing Girth (graph theory) (section)

==Cages==
{{main|Cage (graph theory)}}
A [[cubic graph]] (all vertices have degree three) of girth {{mvar|g}} that is as small as possible is known as a {{mvar|g}}-[[cage (graph theory)|cage]] (or as a {{math|(3,''g'')}}-cage).  The [[Petersen graph]] is the unique 5-cage (it is the smallest cubic graph of girth 5), the [[Heawood graph]] is the unique 6-cage, the [[McGee graph]] is the unique 7-cage and the [[Tutte eight cage]] is the unique 8-cage.<ref>{{citation|first=Andries E.|last=Brouwer|author-link=Andries Brouwer|url=http://www.win.tue.nl/~aeb/drg/graphs/|title=Cages}}. Electronic supplement to the book ''Distance-Regular Graphs'' (Brouwer, Cohen, and Neumaier 1989, Springer-Verlag).</ref> There may exist multiple cages for a given girth. For instance there are three nonisomorphic 10-cages, each with 70 vertices: the [[Balaban 10-cage]], the [[Harries graph]] and the [[Harries–Wong graph]].

<gallery>
Image:Petersen1 tiny.svg|The [[Petersen graph]] has a girth of 5
Image:Heawood_Graph.svg|The [[Heawood graph]] has a girth of 6
Image:McGee graph.svg|The [[McGee graph]] has a girth of 7
Image:Tutte eight cage.svg|The [[Tutte–Coxeter graph]] (''Tutte eight cage'') has a girth of 8
</gallery>