Joy Morris

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We show that the full automorphism group of a circulant digraph of square-free order is either the intersection of two 2-closed groups, each of which is the wreath product of 2-closed groups of smaller degree, or contains a transitive normal subgroup which is the direct product of two 2-closed groups of smaller degree. The work in this paper makes(More)
A balanced graph is a bipartite graph with no induced circuit of length 2 (mod 4). These graphs arise in linear programming. We focus on graph-algebraic properties of balanced graphs to prove a complete classification of balanced Cayley graphs on abelian groups. Moreover, in Section 5 of this paper, we prove that there is no cubic balanced planar graph.(More)
It has been shown that there is a Hamilton cycle in every connected Cayley graph on any group G whose commutator subgroup is cyclic of prime-power order. This note considers connected, vertex-transitive graphs X of order at least 3, such that the automorphism group of X contains a vertex-transitive subgroup G whose commutator subgroup is cyclic of(More)
Let S be a subset of the units in n. Let Γ be a circulant graph of order n (a Cayley graph of n) such that if ij ∈ E(Γ), then i − j (mod n) ∈ S. Toida conjectured that if Γ is another circulant graph of order n, then Γ and Γ are isomorphic if and only if they are isomorphic by a group automorphism of n. In this paper, we prove that Toida's conjecture is(More)
A graph is called a GRR if its automorphism group acts regularly on its vertex-set. Such a graph is necessarily a Cayley graph. God-sil has shown that there are only two infinite families of finite groups that do not admit GRRs: abelian groups and generalised dicyclic groups [4]. Indeed, any Cayley graph on such a group admits specific additional graph(More)