The Balaban10CageGraph, HarriesGraph, and HarriesWongGraph commands return the Balaban 10-cage graph, the Harries graph, and the Harries-Wong graph respectively.

Each of these is an undirected graph with 70 vertices, 105 edges, diameter 6, and girth 10.

Together these graphs comprise the complete list of known (3,10) cage graphs.

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

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

$G≔\mathrm{Balaban10CageGraph}\left(\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 70\; vertices\; and\; 105\; edge(s)}$

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

$10$

$G≔\mathrm{HarriesGraph}\left(\right)$

$G≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 70\; vertices\; and\; 105\; edge(s)}$

$\mathrm{DrawGraph}\left(G\right)$

"Balaban 10-cage", Wikipedia. http://en.wikipedia.org/wiki/Balaban_10-cage

"Harries graph", Wikipedia. http://en.wikipedia.org/wiki/Harries_graph

"Harries-Wong graph", Wikipedia. http://en.wikipedia.org/wiki/Harries-Wong_graph

A. T. Balaban, A trivalent graph of girth ten, J. Combin. Theory Ser. B 12, 1-5. 1972.

M. O'Keefe and P.K. Wong, A smallest graph of girth 10 and valency 3, J. Combin. Theory Ser. B 29 (1980) 91–105.