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Full-Text Articles in Physical Sciences and Mathematics
Bounds On K-Regular Ramanujan Graphs And Separator Theorems, James Skees
Bounds On K-Regular Ramanujan Graphs And Separator Theorems, James Skees
Masters Theses & Specialist Projects
Expander graphs are a family of graphs that are highly connected. Finding explicit examples of expander graphs which are also sparse is a difficult problem. The best type of expander graph in a. certain sense is a Ramanujan graph. Families of graphs that have separator theorems fail to be Ramanujan if the vertex set gets sufficiently large. Using separator theorems to get an estimate on the expanding constant of graphs, we get bounds 011 the number of vertices for such fc-regular graphs in order for them to be Ramanujan.
Loop Edge Estimation In 4-Regular Hamiltonian Graphs, Yale Madden
Loop Edge Estimation In 4-Regular Hamiltonian Graphs, Yale Madden
Masters Theses & Specialist Projects
In knot theory, a knot is defined as a closed, non-self-intersecting curve embedded in three-dimensional space that cannot be untangled to produce a simple planar loop. A mathematical knot is essentially a conventional knot tied with rope where the ends of the rope have been glued together. One way to sample large knots is based on choosing a 4-regular Hamiltonian planar graph. A method for generating rooted 4-regular Hamiltonian planar graphs with n vertices is discussed in this thesis. In the generation process of these graphs, some vertices are introduced that can be easily eliminated from the resulting knot diagram. …