2011/03/30 by Ashraf Daneshkhah, Alice Devillers, Daneshkhah, Ashraf +1
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1103.5846
openalex publication_date 2011/03/30 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
The subdivision graph S(Σ) of a connected graph Σ is constructed by adding a vertex in the middle of each edge. In a previous paper written with Cheryl E. Praeger, we characterised the graphs Σ such that S(Σ) is locally (G,s)-distance transitive for s≤ 2 diam(Σ)-1 and some G≤ Aut(Σ). In this paper, we solve the remaining cases by classifying all the graphs Σ such that the subdivision graphs is locally (G,s)-distance transitive for s≥ 2 diam(Σ) and some G≤ Aut(Σ). In particular, their subdivision graph are always locally G-distance transitive, except for the complete graphs.