On a new cyclicity measure of graphs—The global cyclicity index

On a new cyclicity measure of graphs - The global cyclicity index

Being motivated in terms of mathematical concepts from the theory of electrical networks, Klein & Ivanciuc introduced and studied a new graph-theoretic cyclicity index–the global cyclicity index (Graph cyclicity, excess conductance, and resistance deficit, J. Math. Chem. 30 (2001) 271–287). In this paper, by utilizing techniques from graph theory, electrical network theory and real analysis, we...

Upper bounds for the index of cyclicity of a matrix∗

We derive upper bounds for the index of cyclicity of a matrix as a function of the size of the matrix. This result can be used in the characterization of the ultimate behavior of the sequence of consecutive powers of a matrix in the max-plus algebra, which has maximum and addition as its basic operations. If the matrix is irreducible then it is well known that the ultimate behavior is cyclic. F...

CYCLICITY OF (Z/(p))×

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...