An injective $k$-edge-coloring of a graph $G$ is an assignment colors, i.e. integers in $\{1, \ldots , k\}$, to the edges such that any two each incident with one distinct endpoint third edge, receive colors. The problem determining whether $k$-coloring exists called k-INJECTIVE EDGE-COLORING. We show 3-INJECTIVE EDGE-COLORING NP-complete, even for triangle-free cubic graphs, planar subcubic gr...

In this paper, we study residuated lattices in order to give new characterizations for dense, regular and Boolean elements in residuated lattices and investigate special residuated lattices in order to obtain new characterizations for the directly indecomposable subvariety of Stonean residuated lattices. Free algebra in varieties of Stonean residuated lattices is constructed. We introduce in re...

This paper characterizes the injective and projective objects in the category of directed multigraphs, or quivers. Further, the injective envelope and projective cover of any quiver in this category is constructed.

We present a geometric optimisation framework that can recover fold-over free maps from non-injective initial states using popular flip-preventing distortion energies. Since energies are infinite for folded configurations, we propose new regularisation scheme shifts the singular values of deformation gradient. This allow us to re-use many existing algorithms, especially locally injective method...

Let $R$ be a commutative ring with identity. The purpose of this paper is to introduce and study two classes of modules over $R$, called $mbox{Max}$-injective and $mbox{Max}$-strongly top modules and explore some of their basic properties. Our concern is to extend some properties of $X$-injective and strongly top modules to these classes of modules and obtain some related results.

We compute the K-theory of crossed products rotation algebras Aθ, for any real angle θ, by matrices in SL(2,Z) with infinite order. Using techniques continuous fields, we show that canonical inclusion Aθ into is injective at level K0-groups. then give an explicit set generators K0-groups and tracial ranges concretely.

We investigate and compare four variants of the doublepushout approach to graph transformation. Besides the traditional approach with arbitrary matching and injective right-hand morphisms, we consider three variations by employing injective matching and/or arbitrary right-hand morphisms in rules. For each of the three variations, we clarify whether the well-known commutativity theorems are stil...

Image transforms are used extensively in image processing to convert one image form into another form. These transforms are either point-operation transforms or neighborhood-operation transforms. Injective transforms, also known as reversible or one-to-one transforms, are a subset of point-operation transforms where each intensity value maps to a distinct intensity value. In this paper we prese...