Rose Window Graphs
نویسنده
چکیده
This paper introduces a family of tetravalent graphs called rose window graphs, denoted by Rn(a, r), and investigates their symmetry properties. Four families of these graphs are shown to be edge-transitive and it is conjectured that every Rn(a, r) which is edge-transitive belongs to one of these families. Proofs and conjectures about the size of a dart-stabilizer and about regular maps containing these graphs are also offered.
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The automorphism groups of non-edge-transitive rose window graphs
In this paper, we will determine the full automorphism groups of rose window graphs that are not edge-transitive. As the full automorphism groups of edge-transitive rose window graphs have been determined, this will complete the problem of calculating the full automorphism group of rose window graphs. As a corollary, we determine which rose window graphs are vertex-transitive. Finally, we deter...
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