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Full-Text Articles in Physical Sciences and Mathematics
Symmetries Of Embedded Complete Bipartite Graphs, Erica Flapan, Nicole Lehle, Blake Mellor, Matt Pittluck, Xan Vongsathorn
Symmetries Of Embedded Complete Bipartite Graphs, Erica Flapan, Nicole Lehle, Blake Mellor, Matt Pittluck, Xan Vongsathorn
Blake Mellor
We characterize which automorphisms of an arbitrary complete bipartite graph Kn,m can be induced by a homeomorphism of some embedding of the graph in S3.
Colorings, Determinants And Alexander Polynomials For Spatial Graphs, Terry Kong, Alec Lewald, Blake Mellor, Vadim Pigrish
Colorings, Determinants And Alexander Polynomials For Spatial Graphs, Terry Kong, Alec Lewald, Blake Mellor, Vadim Pigrish
Blake Mellor
A {\em balanced} spatial graph has an integer weight on each edge, so that the directed sum of the weights at each vertex is zero. We describe the Alexander module and polynomial for balanced spatial graphs (originally due to Kinoshita \cite{ki}), and examine their behavior under some common operations on the graph. We use the Alexander module to define the determinant and p-colorings of a balanced spatial graph, and provide examples. We show that the determinant of a spatial graph determines for which p the graph is p-colorable, and that a p-coloring of a graph corresponds to a representation of …