Cayley graphs on non-isomorphic groups
Joy Morris, Adrian Skelton

TL;DR
This paper investigates conditions under which Cayley graphs on abelian groups can also be represented as Cayley graphs on generalized dihedral groups, exploring the relationship between different group structures for the same graph.
Contribution
It provides new criteria for when Cayley graphs on abelian groups can be represented on generalized dihedral groups and vice versa.
Findings
Identifies conditions for Cayley graphs on abelian groups to be represented on generalized dihedral groups
Establishes criteria for when such representations are possible in both directions
Advances understanding of the relationship between different group structures for Cayley graphs
Abstract
A number of authors have studied the question of when a graph can be represented as a Cayley graph on more than one nonisomorphic group. In this paper we give conditions for when a Cayley graph on an abelian group can be represented as a Cayley graph on a generalized dihedral group, and conditions for when the converse is true.
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Taxonomy
TopicsFinite Group Theory Research · Advanced Topics in Algebra · graph theory and CDMA systems
