On Biggs-Smith graph in $\mathcal C$-UH-graph context
Italo Jose Dejter · 2010
A method of construction of $\mathcal C$-ultrahomogeneous (or $\mathcal C$-UH) graphs is applied to the Biggs-Smith graph, which is seen in the process as a $\{C_9\}_{P_4}$-UH graph and a $\{\vec{C_9}\}_{\vec{P_4}}$-UH digraph, to demonstrate the existence of a connected edge-disjoint union $Y$ of 102 tetrahedra, where also $Y=$ union of 102 cuboctahedra with no common squares, having the $\mathcal C$-UH property for ${\mathcal C}=\{K_4\}\cup\{L(Q_3)\}$ and each triangle (resp. edge) shared exactly by two cuboctahedra and one tetrahedron (resp. four cuboctahedra). This $Y$ is the Menger graph of a self-dual $(102_4)$-configuration.