A construction based on the Biggs-Smith graph
نویسنده
چکیده
Departing from the Biggs-Smith graph, we construct a connected 12regular 102-vertex graph Y of diameter 3 that can be presented as the edge-disjoint union of 102 copies of K4 or as the square-disjoint union of 102 cuboctahedra L(Q3), with each edge shared by four L(Q3)s and each triangle shared by two L(Q3)s and a sole copy of K4. Moreover, Y is the non-line-graphical Menger graph of a self-dual (1024)-configuration. Furthermore, Y is a {K4, L(Q3)}K3 -ultrahomogeneous graph.
منابع مشابه
On a Biggs-Smith self-dual (1024)-configuration
A construction based on the Biggs-Smith graph is shown to produce an edge-disjoint union of 102 copies of K4 forming a {K4, L(Q3)}K3 -ultrahomogeneous graph dressed as the non-line-graphical Menger graph of a self-dual (1024)-configuration. This stands in contrast to the selfdual (424)-configuration of [8], whose Menger graph is a non-line-graphical {K4, K2,2,2}K2 -ultrahomogeneous graph.
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