Relative centricity RC values of vertices/atoms are calculated within the Distance Detour and Cluj-Distance criteria on their corresponding Shell transforms. The vertex RC distribution in a molecular graph gives atom equivalence classes, useful in interpretation of NMR spectra. Timed by vertex valences, RC provides a new index, called Centric Connectivity CC, which can be useful in the topologi...

Kengo Matsumoto has introduced λ-graph systems and strong shift equivalence of λ-graph systems [Doc.Math.4 (1999), 285-340]. We associate to a subshift of a subshift a λ-graph system. The strong shift equivalence class of the associated λ-graph system is an invariant of subsystem equivalence. Wolfgang Krieger and Kengo Matsumoto have introduced the λ-entropy of a λ-graph system and have shown i...

We examine the notion of structures and functions in the Ershov difference hierarchy, and of equivalence structures in particular. A equivalence structure A = (A,E) has universe A = ω and an equivalence relation E. The equivalence class [a] of a ∈ A is {b ∈ A : aEb} and the character K of A is {〈k, n〉 ∈ (ω − {0}) : A has at least n classes of size k}. It is known that for any character K, there...

We classify Brauer graph algebras up to derived equivalence by showing that the set of invariants introduced Antipov is complete. These first appeared in representation theory finite groups and can be defined for any suitably decorated on an oriented surface. Motivated connection between gentle we consider A∞-trivial extensions partially wrapped Fukaya categories associated surfaces with bounda...

Graph bundles generalize the notion of covering graphs and graph products. In Imrich et al. (Discrete Math. 167=168 (1998) 393) authors constructed an algorithm that 5nds a presentation as a nontrivial cartesian graph bundle for all graphs that are cartesian graph bundles over triangle-free simple base using the relation ∗ having the square property. An equivalence relation R on the edge set of...

A method for partitioning shapes is described based on a global convexity measure. Its advantages are that its global nature makes it robust to noise, and apart from the number of partitioning cuts no parameters are required. In order to ensure that the method operates correctly on bent or undulating shapes a process is developed that identifies the underlying bending and removes it, straighten...