OddGirth returns the length of the shortest odd cycle in a simple graph.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$G≔\mathrm{SpecialGraphs}\left[\mathrm{HypercubeGraph}\right]\left(3\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; unweighted\; graph\; with\; 8\; vertices\; and\; 12\; edge(s)}$

$H≔\mathrm{Subdivide}\left(G\,\left\{''000''\,''001''\right\}\right)$

$H≔\mathrm{Graph\; 2:\; an\; undirected\; unweighted\; graph\; with\; 9\; vertices\; and\; 13\; edge(s)}$

$\mathrm{Girth}\left(H\right)$

$4$

$\mathrm{OddGirth}\left(H\right)$

$5$