On a {K_4,K_{2,2,2}}-ultrahomogeneous graph
| dc.creator | Dejter, Italo J. | |
| dc.date | 2007-04-11 | |
| dc.date | 2008-10-20 | |
| dc.date.accessioned | 2026-07-07T12:57:17Z | |
| dc.date.available | 2026-07-07T12:57:17Z | |
| dc.description | The existence of a connected 12-regular $\{K_4,K_{2,2,2}\}$-ultrahomogeneous graph $G$ is established, (i.e. each isomorphism between two copies of $K_4$ or $K_{2,2,2}$ in $G$ extends to an automorphism of $G$), with the 42 ordered lines of the Fano plane taken as vertices. This graph $G$ can be expressed in a unique way both as the edge-disjoint union of 42 induced copies of $K_4$ and as the edge-disjoint union of 21 induced copies of $K_{2,2,2}$, with no more copies of $K_4$ or $K_{2,2,2}$ existing in $G$. Moreover, each edge of $G$ is shared by exactly one copy of $K_4$ and one of $K_{2,2,2}$. While the line graphs of $d$-cubes, ($3\le d\in\ZZ$), are $\{K_d, K_{2,2}\}$-ultrahomogeneous, $G$ is not even line-graphical. In addition, the chordless 6-cycles of $G$ are seen to play an interesting role and some self-dual configurations associated to $G$ with 2-arc-transitive, arc-transitive and semisymmetric Levi graphs are considered. | |
| dc.description | 12 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/0704.1493 | |
| dc.identifier | http://arxiv.org/abs/0704.1493 | |
| dc.identifier | Australasian Jour. of Combinatorics, 44 (2009), 63--75 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224877 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C62 | |
| dc.title | On a {K_4,K_{2,2,2}}-ultrahomogeneous graph | |
| dc.type | text |