We give an alternative criterion for ODE equivalence in identical edge homogeneous coupled cell networks. This allows us to give a simple proof of Theorem 10.3 of Aquiar and Dias, which characterizes minimal identical edge homogeneous coupled cell networks. Using our criterion we give a formula for counting homogeneous coupled cell networks up to ODE equivalence. Our criterion is purely graph t...

Querying large data graphs has brought the attention of the research community. Many solutions were proposed, such as Oracle Semantic Technologies, Virtuoso, RDF3X, and C-Store, among others. Although such approaches have shown good performance in queries with medium complexity, they perform poorly when the complexity of the queries increases. In this paper, the authors propose the Graph Signat...

For a connected graph, a subset of vertices of least size whose deletion increases the number of connected components is the vertex connectivity of the graph. A graph with vertex connectivity k is said to be k-vertex connected. Given a k-vertex connected graph G, vertex connectivity augmentation determines a smallest set of edges whose augmentation to G makes it (k + 1)-vertex connected. In thi...

Two edges el and e2 of an undirected graph are cycle-equivalent iff all cycles that contain el also contain e2, i.e., iff el and e2 are a cut-edge pair. The cycle-equivalence classes of the control-flow graph are used in optimizing compilers to speed up ezasting control-flow and data-flow algorithms. While the cycle-equivalence classes can be computed in linear time, we present the first fully ...

A Smarandachely k-signed graph (Smarandachely k-marked graph) is an ordered pair S = (G,σ) (S = (G,μ)), where G = (V, E) is a graph called the underlying graph of S and σ : E → (e1, e2, · · · , ek) (μ : V → (e1, e2, · · · , ek)) is a function, where each ei ∈ {+,−}. Particularly, a Smarandachely 2-singed graph or 2-marked graph is called abbreviated to a singed graph or a marked graph. We chara...

the main goal of the present paper is to extend classical results from the measure theory and dynamical systems to the fuzzy subset setting. in this paper, the notion of  dynamic equivalence relation is introduced and then it is proved that this relation is an equivalence relation. also, a new metric on the collection of all equivalence classes is introduced and it is proved that this metric is...

It is well-known that a finite graph can be viewed, in many respects, as a discrete analogue of a Riemann surface. In this paper, we pursue this analogy further in the context of linear equivalence of divisors. In particular, we formulate and prove a graph-theoretic analogue of the classical Riemann-Roch theorem. We also prove several results, analogous to classical facts about Riemann surfaces...

Two boards are rook equivalent if they have the same number of non-attacking placements for any rooks. Define a equivalence graph on an class Ferrers by specifying that two connected edge you can obtain one moving squares in other board out column and into single column. Given such graph, we characterize which will yield graphs. We also provide some cases where common graphs or not be set board...

Graph reduction is an implementation technique for the lazy λ-calculus. It has been used to implement many non-strict functional languages, such as lazy ML, Gofer and Miranda. Parallel graph reduction allows for concurrent evaluation. In this paper, we present parallel graph reduction as a Chemical Abstract Machine, and show that the resulting testing semantics is adequate wrt testing equivalen...

If G is a claw-free graph, then there is a graph cl(G) such that (i) G is a spanning subgraph of cl(G), (ii) cl(G) is a line graph of a triangle-free graph, and (iii) the length of a longest cycle in G and in cl(G) is the same. A suucient condition for hamiltonicity in claw-free graphs, the equivalence of some conjectures on hamiltonicity in 2-tough graphs and the hamiltonicity of 7-connected c...