In a manner analogous to a commutative ring, the idealbased zero-divisor graph of a commutative semiring R can be defined as the undirected graph ΓI(R) for some ideal I of R. The properties and possible structures of the graph ΓI (R) are studied.

In this article, we obtain an upper bound for the regularity of binomial edge ideal a graph whose every block is either cycle or clique. As consequence, cactus graph. We also identify certain subclass attaining bound.

We determine the arithmetical rank of every edge ideal of a Ferrers graph.

Lattice defects generated by radiation damage can diffuse to grain boundaries (GBs) and be annihilated at GBs. However, the precise role of GBs in annihilating the segregated defects remains unclear. Here, we employed multi-scale models to determine how interstitials are annihilated at small-angle tilt GBs (STGBs) in SiC. First of all, we found the pipe diffusion of interstitials in STGBs is sl...

This is a short survey of the main known results concerning annihilating polynomials for the Witt ring of quadratic forms over a field. 1991 A.M.S. Subject Classification : 11E81, 12F10, 19A22

The Graph Minor Theorem of Robertson and Seymour establishes nonconstructively that many natural graph properties are characterized by a nite set of forbidden substructures, the obstructions for the property. We prove several general theorems regarding the computation of obstruction sets from other information about a family of graphs. The methods can be adapted to other partial orders on graph...

Recently, so called annihilating filer-based low rank Hankel matrix (ALOHA) approach was proposed as a powerful image inpainting method. Based on the observation that smoothness or textures within an image patch corresponds to sparse spectral components in the frequency domain, ALOHA exploits the existence of annihilating filters and the associated rank-deficient Hankel matrices in the image do...