12269815
Angular 2-Structures
The theory of 2-structures forms a convenient framework for investigating graphs. In this paper we investigate the class of angular 2-structures which results by requiring that the primitivity is forbidden on the lowest possible level, i.e. it is required that no substructure on three elements is primitive. The paper presents the basic theory of angular 2-structures and, in particular, the theory of primitive angular 2-structures. We demonstrate that the notion of an angular 2-structure is a well-chosen generalization of the notions of a symmetric graph and a partial order.
40876494
Theory of 2-Structures
The process according to the present invention relates to the production of ferrovanadium alloys. The process comprises melting a charge containing iron and vanadium with a subsequent reduction of iron and vanadium to give a metal melt. In accordance with the present invention, iron and vanadium are reduced substantially completely. The resulting metal melt is poured into a converter and then purged, through the converter bottom, by means of oxygen blowing at a supply rate of oxygen and for a period of time sufficient to produce a slag containing at least 35% by weight of vanadium pentoxide. Thereafter, the metal melt is discharged from the converter, while vanadium and iron are reduced from the resulting slag by the metallothermal method.
34951842
Primitivity is Hereditary for 2-Structures
Abstract It is proved that each primitive 2-structure on n elements ( n ⩾3) contains a primitive substructure on either ( n −1) or ( n −2) elements.
33004065
Pancyclicity in switching classes
Abstract Switching classes of graphs were introduced by van Lint and Seidel in the context of equiangular lines in elliptic geometry. We show that every switching class, except the class of all complete bipartite graphs, contains a pancyclic graph. This implies that deciding whether a switching class contains a hamiltonian graph can be done in polynomial time (as was noted by Kratochvil et al. (1992)) although this problem is NP-complete for graphs.
39431424
Incremental construction of 2-structures
Abstract A labeled 2-structure g is an edge-labeled directed graph with a reversibility condition on the labels. Each labeled 2-structure g can be represented as a tree, the prime tree of g. We characterize a labeled 2-structure h in terms of the prime tree of a labeled 2-structure g which results from h by removing one element from h. This leads to an O(n3) algorithm for the construction of the prime tree.
37770747
Transitivity of local complementation and switching on graphs
Abstract The operations complementation C , local complementation λ x , and switching σ x for the vertices x of a finite undirected graph are considered. The operation λ x complements the subgraph induced by the neighbourhood of x in the given graph, and the switching σ x changes the neighbourhood of x to its complement vertex set. It is proved that the compositions δ x = λ x C (for vertices x ∈ D ) generate a transitive group on the graphs with vertex set D , that is, for any two graphs g and h on D , there exists a composition α of operations δ x such that h = α ( g ). It is also shown that the compositions τ x = λ x σ x (for x ∈ D ) generate a transitive group on the graphs.
816336
Actor grammars
Actor systems are a model of massively parallel systems based on asynchronous message passing. This paper presents a formalism for a restricted version of actor systems in the framework of graph grammars. To this aim actor grammars are introduced, motivated, and illustrated by examples. Some of the basic properties pertinent to graph transformations in actor grammars are discussed.
11853375
Edge-Label Controlled Graph Grammars
Abstract We introduce a graph-grammar model based on edge-replacement, where both the rewriting and the embedding mechanisms are controlled by edge labels. The general power of this model is established—it turns out to have the complete power of recursive enumerability (in a sense to be made precise in the paper). In order to understand where this power originates, we identify three basic features of the embedding mechanism and examine how restrictions on these features affect the generative power. In particular, by imposing restrictions on all three features simultaneously, we obtain a graph-grammar model that was previously introduced by Kreowski and Habel.
43370814
Boundary NLC Graph Grammars-Basic Definitions, Normal Forms, and Complexity
Node label controlled (NLC) grammars are graph grammars (operating on node labeled undirected graphs) which rewrite single nodes only and establish connections between the embedded graph and the neighbors of the rewritten node on the basis of the labels of the involved nodes only. They define (possibly infinite) languages of undirected node labeled graphs (or, if we just omit the labels, languages of unlabeled graphs). Here we consider a restriction of NLC grammars, so-called boundary NLC (BNLC) grammars , distinguished by the property that whenever in a graph already generated two nodes may be rewritten, then these nodes are not adjacent. The graph languages generated by this type of grammars are called BNLC languages . Although we show that this restriction leads to a smaller class of languages, still enough generative power remains to define interesting graph languages. For example, trees, complete bipartite graphs, maximal outerplanar graphs, k -trees, graphs of bandwidth ⩽ k , graphs of cyclic bandwidth ⩽ k , graphs of binary tree bandwidth ⩽ k , graphs of cutwidth ⩽ k (always for a fixed positive integer k ) turn out all to be BNLC languages. We prove a number of normal forms for BNLC grammars and then we indicate their usefulness by various applications. In particular, we show that for connected graphs of bounded degree the membership problem for BNLC languages is solvable in deterministic polynomial time.
38594002
Using String Languages to Describe Picture Languages
A picture is a set of unit lines from the Cartesian plane considered as a square grid. A word over the alphabet l, r, u, d is a picture description in the sense that it represents a traversal of a picture where the interpretation of the symbols l, r, u, d, is: l go one unit line to the left of the current point r go one unit line to the right of the current point u go one unit line up from the current point, and d go one unit line down from the current point. A set of picture descriptions forms a picture description language . This paper investigates the basic properties of pictures and picture description languages from the formal language theory point of view.
37152120
Transition Systems, Event Structures and Unfoldings
A subclass of transition systems called elementary transition systems can be identified with the help of axioms based on a structural notion called regions. Elementary transition systems have been shown to be the transition system model of a basic system model of net theory called elementary net systems. Here we show that by smoothly strengthening the regional axioms for elementary transition systems, one obtains a subclass called occurrence transition system. We then prove that occurrence transition systems are the transition system model of yet another basic model of concurrency, namely, prime event structures. We then propose an operation of unfolding elementary transition systems into occurrence transition systems, We prove that it is "correct" in a strong categorical sense.