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Full-Text Articles in Mathematics
Complete Graphs Whose Topological Symmetry Groups Are Polyhedral, Eric Flapan, Blake Mellor, Ramin Naimi
Complete Graphs Whose Topological Symmetry Groups Are Polyhedral, Eric Flapan, Blake Mellor, Ramin Naimi
Mathematics Faculty Works
We determine for which m the complete graph Km has an embedding in S3 whose topological symmetry group is isomorphic to one of the polyhedral groups A4, A5 or S4.
Intrinsic Linking And Knotting In Virtual Spatial Graphs, Thomas Fleming, Blake Mellor
Intrinsic Linking And Knotting In Virtual Spatial Graphs, Thomas Fleming, Blake Mellor
Mathematics Faculty Works
We introduce a notion of intrinsic linking and knotting for virtual spatial graphs. Our theory gives two filtrations of the set of all graphs, allowing us to measure, in a sense, how intrinsically linked or knotted a graph is; we show that these filtrations are descending and nonterminating. We also provide several examples of intrinsically virtually linked and knotted graphs. As a byproduct, we introduce the virtual unknotting number of a knot, and show that any knot with nontrivial Jones polynomial has virtual unknotting number at least 2.