Graph theory, symmetry and inorganic solids

Evolutionary graph theory: breaking the symmetry between interaction and replacement.

We study evolutionary dynamics in a population whose structure is given by two graphs: the interaction graph determines who plays with whom in an evolutionary game; the replacement graph specifies the geometry of evolutionary competition and updating. First, we calculate the fixation probabilities of frequency dependent selection between two strategies or phenotypes. We consider three different...

Symmetry Groups of Platonic Solids

Phase transitions in solids of diperiodic symmetry.

All isotropy subgroups (and thus all quasicontinuous symmetry changes) corresponding to k points of symmetry have been obtained for the 80 diperiodic space groups. The detailed information for such phase transitions is given here for the diperiodic space group I'———.Only two distinct images (sets of representation matrices) occur for this example yielding Landau-Ginzburg-Wilson (LGW) Hamiltonia...

Graph homomorphisms: structure and symmetry

This paper is the first part of an introduction to the subject of graph homomorphism in the mixed form of a course and a survey. We give the basic definitions, examples and uses of graph homomorphisms and mention some results that consider the structure and some parameters of the graphs involved. We discuss vertex transitive graphs and Cayley graphs and their rather fundamental role in some asp...

Noether Symmetry in f(T) Theory at the anisotropic universe

As it is well known, symmetry plays a crucial role in the theoretical physics. On other hand, the Noether symmetry is a useful procedure to select models motivated at a fundamental level, and to discover the exact solution to the given lagrangian. In this work, Noether symmetry in f(T) theory on a spatially homogeneous and anisotropic Bianchi type I universe is considered. We discuss the Lagran...