Dedicated to the memory of Prof. Dom de Caen Abstract. Given λ and μ, it is shown that, unless one of the relations (λ− μ)2 = 4μ, λ− μ = −2, (λ− μ)2 + 2(λ− μ) = 4μ is satisfied, there are only finitely many parameter sets (v, k, λ, μ) for which a strongly regular graph with these parameters could exist. This result is used to prove as special cases a number of results which have appeared in pre...

The CONCERTO project, primarily concerned with the annotation of texts for their conceptual content, combines automatic linguistic analysis with manual annotation to ensure the accuracy of fact extraction, and to encode content in a rich knowledge representation framework. The system provides annotation tools, automatic multi-level linguistic analysis modules, a partial parsing formalism with a...

Even the fastest SMT solvers have performance problems with regular expressions from real programs. Because these performance issues often arise from the problem representation (e.g. non-deterministic finite automata get determinized and regular expressions get unrolled), we revisit Boolean finite automata, which allow for the direct and natural representation of any Boolean combination of regu...

In this note we show that there is a unique distance-regular graph with intersection array {280, 243, 144, 10; 1, 8, 90, 280}.

In this paper, we examine the structure of vertexand edge-transitive strongly regular graphs, using normal quotient reduction. We show that the irreducible graphs in this family have quasiprimitive automorphism groups, and prove (using the Classification of Finite Simple Groups) that no graph in this family has a holomorphic simple automorphism group. We also find some constraints on the parame...

The purpose of this paper is to construct the solution of self-adjoint boundary value problems on finite networks. To this end, we obtain explicit expressions of the Green functions for all different boundary value problems. The method consists in reducing each boundary value problem either to a Dirichlet problem or to a Poisson equation on a new network closely related with the former boundary...

We give a construction of strongly regular Cayley graphs on finite fields Fq by using union of cyclotomic classes and index 4 Gauss sums. In particular, we obtain two infinite families of strongly regular graphs with new parameters.

It is known that a strongly regular semi-Cayley graph (with respect to a group G) corresponds to a triple of subsets (C, D, D') of G. Such a triple (C, D, D') is called a partial difference triple. First, we study the case when D U D' is contained in a proper normal subgroup of G. We basically determine all possible partial difference triples in this case. In fact, when \G\ f 8 nor 25, all part...

We enumerate the independent sets of several classes of regular and almost regular graphs and compute the corresponding generating functions. We also note the relations between these graphs and other combinatorial objects and, in some cases, construct the corresponding bijections.

In this paper, we are giving MATLAB program to find the energy and Wiener index of unit graphs. Our program demonstrates an intrinsic relationship between the elements of ring and structural properties of graphs. The unit graph G(Zn) turns out to be strongly regular when n = 2k. Several new directions for further research are also indicated by means of raising problems.