The degree set of a graph is the set of its degrees. Kapoor et al. [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. Furthermore, the minimum order of such a graph is determined. A graph is 2-self- centered if its radius and diameter are two. In this paper for ...

Abstract We investigate the topological structures of Galois covers surfaces minimal degree (i.e., n ) in . prove that for , any are simply‐connected general type.

We describe a simple unsupervised technique for learning morphology by identifying hubs in an automaton. For our purposes, a hub is a node in a graph with in-degree greater than one and out-degree greater than one. We create a word-trie, transform it into a minimal DFA, then identify hubs. Those hubs mark the boundary between root and suffix, achieving similar performance to more complex mixtur...

Let k(~x) := k(x1, . . . , xn) be a finitely generated extension field of some field k, and denote by k(~g) := k(g1, . . . , gr) an intermediate field of k(~x)/k generated over k by some elements g1, . . . , gr ∈ k(~x). So geometrically, we may take ~g for rational functions on the variety determined by the generic point (~x). To determine whether the extension k(~x)/k(~g) is transcendental or ...

Two properties of the Co-spectrum of the Joint spectrum of infinitely many abstract structures are presented — a Minimal Pair type theorem and the existence of a Quasi-Minimal degree with respect to the Joint spectrum of the structures.

Two properties of the Co-Spectrum of the Joint Spectrum of finitely many abstract structures are presented a Minimal Pair type theorem and the existence of a Quasi-Minimal degree with respect to the Joint Spectrum of the structures.