Disk-cyclicity and codisk-cyclicity of certain shift operators

CYCLICITY OF (Z/(p))×

Cyclicity of graphs

The cyclicity of a graph is the largest integer n for which the graph is contractible to the cycle on n vertices. By analyzing the cycle space of a graph, we establish upper and lower bounds on cyclicity. These bounds facilitate the computation of cyclicity for several classes of graphs, including chordal graphs, complete n-partite graphs, n-cubes, products of trees and cycles, and planar graph...

Cyclicity versus Center Problem

We prove that there are one-parameter families of planar differential equations for which the center problem has a trivial solution and on the other hand the cyclicity of the weak focus is arbitrarily high. We illustrate this phenomenon in several examples for which this cyclicity is computed.

The cyclicity of a hypergraph

The cyclicity of a hypergraph is an e ciently computable integer that extends the notion of the cyclomatic number of a graph The formula for the cyclicity is suggested by the join invariant of an acyclic hypergraph which is the multiset of all joining sets in any of its join trees Once we gure out how the multiplicity of a joining set depends on the structure of the acyclic hypergraph we de ne ...

The cyclicity of a hypergraph

The cyclicity of a hypergraph is an efficiently computable integer that extends the notion of the cyclomatic number of a graph. Generalizing the notion of the degree of a node in a graph, we define the star articulation degree of a subedge in a hypergraph, and then use it to set up the expression for the cyclicity. The basic properties of cyclicity are that it is zero on acyclic hypergraphs and...