The algebra of basic covers of a graph G, denoted by Ā(G), was introduced by Herzog as a suitable quotient of the vertex cover algebra. In this paper we compute the Krull dimension of Ā(G) in terms of the combinatorics of G. As a consequence, we get new upper bounds on the arithmetical rank of monomial ideals of pure codimension 2. Furthermore, we show that if the graph is bipartite, then Ā(G) ...

We study the combinatorics of constructing non-singular geometrically irreducible projective curves that do not admit rational points over finite solvable extensions of the base field. A graph is without solvable orbits if its group of automorphisms acts on each of its orbits through a non-solvable quotient. We prove that there is a connected graph without solvable orbits of cyclomatic number c...

Spatial filtering for EEG feature extraction and classification is an important tool in brain-computer interface. However, there is generally no established theory that links spatial filtering directly to Bayes classification error. To address this issue, this paper proposes and studies a Bayesian analysis theory for spatial filtering in relation to Bayes error. Following the maximum entropy pr...

The authors prove that a proper monomial holomorphic mapping from the two-ball to the N-ball has degree at most 2N 3, and that this result is sharp. The authors first show that certain group-invariant polynomials (related to Lucas polynomials) achieve the bound. To establish the bound the authors introduce a graph-theoretic approach that requires determining the number of sinks in a directed gr...

A graph generator is a tool which allows to create graph-like data whose structural properties are very similar those found in real world networks. This paper presents two methods generate graphs with power-law edge distribution based on the MapReduce processing model that can be easily implemented run top of Apache Hadoop. The proposed allow generation directed and undirected distributed witho...

The power graph P(G) of a group G is with vertex set G, where two vertices u and v are adjacent if only u≠v um=v or vm=u for some positive integer m. In this paper, we raise study the following question: For which natural numbers n every groups order isomorphic graphs isomorphic? particular, it proved that all such odd number cube-free also they not multiples 16 in general. Moreover, show finit...