2009/04/07 by Italo J. Dejter, Dejter, Italo J. · 1 citation
Computer Science · Engineering · Mathematics · #05B30 #05C20 #05C38 #05C62 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.CO #msc:05B30 #msc:05C20 #msc:05C38 #msc:05C62
paper · pdf · doi:10.48550/arxiv.0904.1096
11 pages, 3 figures, 4 tables
openalex publication_date 2009/04/07 · arxiv created 2012/06/14 · arxiv updated 2012/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Like the Coxeter graph became reattached into the Klein graph in [2], the Levi graphs of the 93 and 103 self-dual configurations, known as the Pappus and Desargues (k-transitive) graphs \mathcal P and \mathcal D (where k=3), also admit reattachments of the distance-(k-1) graphs of half of their oriented shortest cycles via orientation assignments on their common (k-1)-arcs, concurrent for \mathcal P and opposite for \mathcal D, now into 2 disjoint copies of their corresponding Menger graphs. Here, \mathcal P is the unique cubic distance-transitive (or CDT) graph with the concurrent-reattachment behavior while \mathcal D is one of 7 CDT graphs with the opposite-reattachment behavior, that include the Coxeter graph. Thus, \mathcal P and \mathcal D confront each other in these respects, obtained via \mathcal C-ultrahomogeneous graph techniques [3,4] that allow to characterize the obtained reattachment Menger graphs in the same terms.