Journal article

Classifying a family of symmetric graphs

SM Zhou

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | AUSTRALIAN MATHEMATICS PUBL ASSOC INC | Published : 2001

Abstract

Let Γ be a G-symmetric graph admitting a nontrivial G-invariant partition B of block size v. For blocks B, C of B adjacent in the quotient graph ΓB, let k be the number of vertices in B adjacent to at least one vertex in C. In this paper we classify all possibilities for (Γ, ΓB, G) in the case where k = v - 1 ≥ 2 and B(α) = B(β) for adjacent vertices α, β of Γ, where for a vertex of Γ, say γ ∈ B, B(γ) denotes the set of blocks C such that γ is the only vertex in B not adjacent to any vertex in C.

University of Melbourne Researchers