Balaban10CageGraph - Maple Help

GraphTheory[SpecialGraphs]

 Balaban10CageGraph
 construct Balaban 10-cage graph
 HarriesGraph
 construct Harries graph
 HarriesWongGraph
 construct Harries-Wong graph

 Calling Sequence Balaban10CageGraph() HarriesGraph() HarriesWongGraph()

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{with}\left(\mathrm{SpecialGraphs}\right):$
 > $G≔\mathrm{Balaban10CageGraph}\left(\right)$
 ${G}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 70 vertices and 105 edge\left(s\right)}}$ (1)
 > $\mathrm{Girth}\left(G\right)$
 ${10}$ (2)
 > $G≔\mathrm{HarriesGraph}\left(\right)$
 ${G}{≔}{\mathrm{Graph 2: an undirected unweighted graph with 70 vertices and 105 edge\left(s\right)}}$ (3)
 > $\mathrm{DrawGraph}\left(G\right)$

References

 "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.