There are fast known algorithms to compute the transitive closure of a fuzzy relation, but there are only a few different algorithms that compute T-transitive low approximations of a fuzzy relation. A fast method to compute a T-transitive low approximation of a reflexive and symmetric fuzzy relation is given for any continuous tnorm, spending O(n) time.

This paper presents a new algorithm to classify all transitive subgroups of the symmetric group up to conjugacy. It has been used to determine the transitive groups of degree up to 30.

A characterisation is given of edge-transitive Cayley graphs of valency 4 on odd number of vertices. The characterisation is then applied to solve several problems in the area of edge-transitive graphs: answering a question proposed by Xu (1998) regarding normal Cayley graphs; providing a method for constructing edge-transitive graphs of valency 4 with arbitrarily large vertex-stabiliser; const...

It is given a new algorithm to compute a lower T-transitive approximation of a fuzzy relation that preserves symmetry. Given a reflexive and symmetric fuzzy relation, the new algorithm computes a T-indistinguishability that is contained in the fuzzy relation. It has been developed a C++ program that generates random symmetric fuzzy relations or random symmetric and reflexive fuzzy relations and...

This paper deals with flag-transitive non-symmetric 2-designs with (r, λ) = 1. We prove that if D is a non-trivial non-symmetric 2-(v, k, λ) design with (r, λ) = 1 and G 6 Aut(D) is flag-transitive with Soc(G) = An for n > 5, then D is a 2-(6, 3, 2) design, the projective space PG(3, 2), or a 2-(10, 6, 5) design.

In this paper we introduce and study a type of Cayley graph – subnormal graph. We prove that 2-arc transitive is normal or cover complete bipartite $\mathbf{K}_{p^d,p^d}$ with $p$ prime. Then obtain generic method for constructing half-symmetric (namely edge but not arc transitive) graphs.

A recent paper of O’Reilly Regueiro obtained an explicit upper bound on the number of points of a flagtransitive, point-imprimitive, symmetric design in terms of the number of blocks containing two points. We improve that upper bound and give a complete list of feasible parameter sequences for such designs for which two points lie in at most ten blocks. Classifications are available for some of...

In this paper we give a classification of a family of symmetric graphs with complete 2-arc transitive quotients. Of particular interest are two subfamilies of graphs which admit an arc-transitive action of a projective linear group. The graphs in these subfamilies can be defined in terms of the cross ratio of certain 4-tuples of elements of a finite projective line, and thus may be called the s...