2014/03/18 by A. Gardiner, Cheryl E. Praeger, Gardiner, A. +1
Computer Science · Engineering · Mathematics · #05C25 #20B25 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1403.4387
openalex publication_date 2014/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Γ be a G-symmetric graph with vertex set V. We suppose that V admits a G-partition B = \ B0, ... , Bb \, with parts of size v, and that the quotient graph induced on \mathcal B is a complete graph of order b+1. Then, for each pair of distinct suffices i, j, the graph induced on the union Bi∪ Bj is bipartite with each vertex of valency 0 or t (a constant). When t=1, it was shown earlier how a flag-transitive 1-design D(Bi) induced on a part Bi can sometimes be used to classify possible triples (Γ, G, \mathcal B). Here we extend these ideas to t > 1 and prove that, if the group induced by G on a part Bi is 2-transitive and the "blocks" of D(Bi) have size less than v, then either (i) v < b, or (ii) the triple (Γ, G, \mathcal B) is known explicitly.