Acyclic covers

Induced Acyclic Graphoidal Covers in a Graph

An induced acyclic graphoidal cover of a graph G is a collection ψ of open paths in G such that every path in ψ has atleast two vertices, every vertex of G is an internal vertex of at most one path in ψ, every edge of G is in exactly one path in ψ and every member of ψ is an induced path. The minimum cardinality of an induced acyclic graphoidal cover of G is called the induced acyclic graphoida...

Simple acyclic graphoidal covers in a graph

An Algorithm for Counting the Number of Edge Covers on Acyclic Graphs

Counting the number of edge covers on graphs, denoted as the #Edge Covers problem, is well known to be #Pcomplete. In this paper, we present an algorithm that compute the number of edge covers in polynomial time if and only if the graph is acyclic. Our algorithm is based on a post-order traversal of the spanning tree of the original graph.

The existence totally reflexive covers

Let $R$ be a commutative Noetherian ring. We prove that  over a local ring $R$ every finitely generated $R$-module $M$ of finite Gorenstein projective dimension has a Gorenstein projective cover$varphi:C rightarrow M$ such that $C$ is finitely generated and the projective dimension of $Kervarphi$ is finite and $varphi$ is surjective.

Non-Abelian Sequenceable Groups Involving ?-Covers

A non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized Fibonacci sequence , , , . A remarkable application of this definition may be find on the study of random covers in the cryptography. The 2-step generalized sequences for the dihedral groups studi...