On a $\vec{C}_4$-ultrahomogeneous oriented graph

Details On a $\vec{C}_4$-ultrahomogeneous oriented graph On a $\vec{C}_4$-ultrahomogeneous oriented graph

2009-05-19

arxiv.org/abs/0905.3172v6

Mathematics

Combinatorics

4 pages, 2 figures, 2 tables

Scientific paper

The notion of a $\mathcal C$-ultrahomogeneous graph, due to Isaksen et al., is adapted for digraphs, and subsequently a strongly connected $\vec{C}_4$-ultrahomogeneous oriented graph on 168 vertices and 126 pairwise arc-disjoint 4-cycles is presented, with regular indegree and outdegree 3 and no circuits of lengths 2 and 3, by altering a definition of the Coxeter graph via pencils of ordered lines of the Fano plane in which pencils are replaced by ordered pencils.

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