The partitioning of graphs is a frequently occurring problem in science and engineering. The spectral graph partitioning method is a promising heuristic method for this class of problems. Its main disadvantage is the large computing time required to solve a special eigenproblem. Here a simple and efficient method is proposed to reduce this computing time. This method is based on the conjugate g...

We deene a new Markov chain on (proper) k-colourings of graphs, and relate its convergence properties to the maximum degree of the graph. The chain is shown to have bounds on convergence time appreciably better than those for the well-known Jerrum/Salas{Sokal chain in most circumstances. For the case k = 22, we provide a dramatic decrease in running time. We also show improvements whenever the ...

Error-correcting graph isomorphism has been found useful in numerous pattern recognition applications. This paper presents a genetic-based search approach that adopts genetic algorithms as the searching criteria to solve the problem of error-correcting graph isomorphism. By applying genetic algorithms, some local search strategies are amalgamated to improve convergence speed. Besides, a selecti...

In this paper, a local feedback control strategy is devised to drive a group of nonholonomic unicycle-type vehicles to a rendezvous point. The proposed control law is continuous and time-invariant. Using tools from graph theory, convergence and ultimate boundedness properties of the overall system are examined. Similar to the results for the rendezvous problem for vehicles governed by linear dy...

We define a new Markov chain on (proper) k-colourings of graphs, and relate its convergence properties to the maximum degree ∆ of the graph. The chain is shown to have bounds on convergence time appreciably better than those for the wellknown Jerrum/Salas–Sokal chain in most circumstances. For the case k = 2∆, we provide a dramatic decrease in running time. We also show improvements whenever th...

The purpose of this paper is to give convergence theorems both for closed convex set valued and relative fuzzy valued martingales, and suband supermartingales. These kinds of martingales, suband super-martingales are the extension of classical real valued martingales, suband super-martingales. Here we compare two kinds of convergences, in the Hausdor metric and in the Kuratowski-Mosco sense. We...

The colored neighborhood metric for sparse graphs was introduced by Bollobás and Riordan [8]. The corresponding convergence notion refines a convergence notion introduced by Benjamini and Schramm [6]. We prove that even in this refined sense, the limit of a convergent graph sequence (with uniformly bounded degree) can be represented by a graphing. We study various topics related to this converg...

Fundamental to the theory of continued fractions is fact that every infinite fraction with positive integer coefficients converges; however, it unknown precisely which (not necessarily positive) converge. Here we present a simple test determines whether an converges or diverges. In addition, for convergent specifies limit rational irrational. An attractive way visualise model them as paths ...