Abstract We characterize seven valent symmetric graphs of order 2 p q n 2p{q}^{n} with < p\lt q odd primes, extending a few previous results. Moreover, consequence partially generalizes the result Conder, Li and Potočnik [ On o...

Preference relations are at the heart of many fundamental concepts in artificial intelligence, ranging from utility comparisons, to defeat among strategies and relative plausibility states, just mention a few. Reasoning about such has been object extensive research wealth formalisms exist express reason them. One formalism is conditional logic, which focuses on reasoning “best” alternatives acc...

There is a familiar construction with two finite, transitive permutation groups as input and a finite, transitive permutation group, called their wreath product, as output. The corresponding 'imprimitive wreath decomposition concept is the first subject of this paper. A formal definition is adopted and an overview obtained for all such decompositions of any given finite, transitive group. The r...

As a consequence of the classification of the finite simple groups, it has been possible in recent years to characterize Steiner t-designs, that is t-(v, k,1) designs, mainly for t = 2, admitting groups of automorphisms with sufficiently strong symmetry properties. However, despite the finite simple group classification, for Steiner t-designs with t > 2 most of these characterizations have rema...

A general method is described which gives rise to highly symmetric tessellations of the Cantor sphere, i.e., the 2-sphere with the Cantor set removed and endowed with the hyperbolic geometry with constant negative curvature. These tessellations correspond to almost vertextransitive planar graphs with infinitely many ends. Their isometry groups have infinitely many ends and are free products wit...

A criterion given by Castejon-Amenedo and MacCallum (1990) for the existence of (locally) hypersurface-orthogonal generators of an orthogonally-transitive two-parameter Abelian group of motions (a G2I) in spacetime is re-expressed as a test for linear dependence with constant coefficients between the three components of the metric in the orbits in canonical coordinates. In general, it is shown ...

Problems labeled ! are important and must be mastered. are harder and cover interesting advanced material that is not properly part of this course. are tangential to the course but cover material that is useful elsewhere. Background A (binary) relation is a set of ordered pairs Two important types of relations are equivalences and (partial) orders: • Equivalence relations are – reflexive (∀x)(x...