A graph is 1-regular if its automorphism group acts regularly on the set of its arcs. Miller [J. Comb. Theory, B, 10 (1971), 163–182] constructed an infinite family of cubic 1-regular graphs of order 2p, where p ≥ 13 is a prime congruent to 1 modulo 3. Marušič and Xu [J. Graph Theory, 25 (1997), 133– 138] found a relation between cubic 1-regular graphs and tetravalent half-transitive graphs wit...

We construct twelve infinite families of pseudocyclic and non-amorphic association schemes, in which each nontrivial relation is a strongly regular graph. Three of the twelve families generalize the counterexamples to A. V. Ivanov’s conjecture by Ikuta and Munemasa [13].

We show that the cartesian closed category of compactly generated Hausdorff spaces is regular, but is neither exact, nor locally cartesian closed. In fact we find a coequalizer of an equivalence relation which is not stable under pullbacks.

A norm inequality is proved for elements of a star algebra so that the algebra is noncommutative. In particular, a relation between maximal and minimal extensions of regular norm on a C∗-algebra is established.

Regularities in databases are directly useful for knowledge discovery and data summarization. As a mathematical background, relational algebra helped for discovering the main data structures and existing dependencies between the different attributes in a relational database. Functional, difunctional and other kinds of dependencies in a relational database describe invariant regular structures t...

We consider the problem of computing measure a regular set infinite binary trees. While general case remains unsolved, we show that language can be computed when is given in one following three formalisms: first-order formula with no descendant relation; Boolean combination conjunctive queries (with relation); or by non-deterministic safety tree automaton. Additionally, first two cases always r...