The possibilities for circuits of length 4 to appear together in a cubic bigraph are classified. That has consequences on the structure of minimally 1-factorable regular bigraphs, i.e. those in which each 1-factor lies in precisely one 1-factorization. We characterize minimally 1-factorable...

We define an between finite simple graphs and use it to define an equivalence relation on the set of natural numbers. The least integers of the equivalence classes serve as canonical code numbers for graphs and this new integer sequence we call the sequence of Characterizations of the...

This paper is about the way to transform any equation into other equations. Moreover, except from that this method allows the transformation of any equation into any other form, there is and the transformation of Cartesian axes into transformed axes. Then, it is plausible with the transformed...

A new approach to the problem is presented. The difficulty of the problem is characterized by the existence of two kinds of chaining processes. A conjecture claiming that the two examined chaining are the only possible is formulated. Should such conjecture be true, the approach could be...

We propose a new graph metric and study its properties. In contrast to the standard geodesic distance in connected graphs, it takes into account all paths between vertices. Simple formulas for the increments of forest distances under basic transformations of a weighted multigraph are presented...

In a landscape composed of randomly distributed sites in Euclidean space, a walker ("tourist") goes to the nearest one that has not been visited in the last steps. This procedure leads to trajectories composed of a transient part and a final cyclic attractor of period The tourist walk presents a...

The benefits of a recently proposed method to approximate hard optimization problems are demonstrated on the graph partitioning problem. The performance of this new method, called Extremal Optimization, is compared to Simulated Annealing in extensive numerical simulations. While generally a...