We introduce a process where connected rooted multigraph evolves by splitting events on its vertices, occurring randomly in continuous time. When vertex splits, incoming edges are assigned between offspring and Poisson random number of added them. The is parametrised positive real λ which governs the limiting average degree. show that for each value there unique M(λ) invariant under this evolut...

Image hashing is the process of associating a short vector of bits to an image. The resulting summaries are useful in many applications including image indexing, image authentication and pattern recognition. These hashes need to be invariant under transformations of the image that result in similar visual content, but should drastically differ for conceptually distinct contents. This paper prop...

A weighting of vertices of a graph is admissible if there exists an edge weighting such that the weight of each vertex equals the sum of weights of its incident edges. Given an admissible vertex weighting of a graph, an invariant set is an edge set such that the sum of the weights of its edges is the same for every edge weighting, and a nonempty invariant set is minimal if none of its nonempty ...

The graph isomorphism problem is to determine whether two given graphs are iso-morphic or not. In this paper, we present a new graph invariant, called the probability propagation matrix. By means of this graph invariant, we present a heuristic algorithm for the problem. The algorithm is easy to implement and highly parallelizable.

Given a directed graph, there exists a universal operator algebra and universal C-algebra associated to the directed graph. In this paper we give intrinsic constructions of these objects. We provide an explicit construction for the maximal C-algebra of an operator algebra. We also discuss uniqueness of the universal algebras for finite graphs, showing that for finite graphs the graph is an isom...

We study quasiperiodically forced circle homeomorphisms and derive a basic classification with respect to the invariant ergodic measures for such systems: Either there exists an invariant graph and every invariant ergodic measure is associated to some invariant graph, or the system is uniquely ergodic. This immediately verifies an observation which is well-known from numerical studies, namely t...