We present a new approach to analysing finite graphs which admit a vertex intransitive group of automorphisms G and are either locally (G, s)– arc transitive for s ≥ 2 or G–locally primitive. Such graphs are bipartite with the two parts of the bipartition being the orbits of G. Given a normal subgroup N which is intransitive on both parts of the bipartition, we show that taking quotients with r...

The results of J. Širáň and the first author (Australasian J. Combin. 10 (1994)) are generalized, and new formulas for the number of closed walks of length p or pq, where p and q are primes, valid for all vertex-transitive graphs are found. Based on these formulas, several simple tests for vertex-transitivity are presented, as well as lower bounds on the orders of the smallest vertexand arc-tra...

We introduce PDD (Pair Distance Distribution), a novel corpus-based model of semantic representation. Most corpus-based models are VSMs (Vector Space Models), which while being successful, suffer from both practical and theoretical shortcomings. VSM models produce very large, sparse matrices, and dimensionality reduction is usually performed, leading to high computational complexity, and obscur...

This paper shows that the subtyping relation of a higher-order lambda calculus, F ! , is anti-symmetric. It exhibits the rst such proof, establishing in the process that the subtyping relation is a partial order| reeexive, transitive and anti-symmetric. While a sub-typing relation is reeexive and transitive by deeni-tion, anti-symmetry is a derived property. The result, which may seem obvious t...

This paper gives the first proof that the subtyping relation of a higherorder lambda calculus, F ≤, is anti-symmetric, establishing in the process that the subtyping relation is a partial order—reflexive, transitive, and anti-symmetric up to β-equality. While a subtyping relation is reflexive and transitive by definition, anti-symmetry is a derived property. The result, which may seem obvious t...

The property of transitivity is one of the most important for fuzzy binary relations, especially in the cases when they are used for the representation of real life similarity or ordering information. As far as the algorithmic part of the actual calculation of the transitive closure of such relations is concerned, works in the literature mainly focus on crisp symmetric relations, paying little ...