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

Abstract

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.

4 pages, 2 figures, 2 tables

References in corpus (1)

• On a {K_4,K_{2,2,2}}-ultrahomogeneous graph