Molecular descriptors are being widely used in QSAR/QSPR studies in chemistry and drug designing as well as modeling of compounds. Different topological descriptors have been formulated to investigate the physio chemical properties and chemical reactivity of compounds. In this article we gave exact relations for first and second Zagreb index, hyper Zagreb index, multiplicative Zagreb indices as well as first and second Zagreb polynomials for some benzenoid systems.

In chemical graph theory, a single numeric number related to a chemical structure is called a topological descriptor or topological index of a graph. In this paper, we compute analytically certain topological indices for H-Naphtalenic nanosheet like Randic index, first Zagreb index, second Zagreb index, geometric arithmetic index, atom bond connectivity index, sum connectivity index and hyper-Zagreb index using edge partition technique. The first multiple Zagreb index and the second multiple Zagreb index of the nanosheet are also discussed in this paper.

We present an algorithm to compute a primary decomposition of an ideal in a polynomial ring over the integers. For this purpose we use algorithms for primary decomposition in polynomial rings over the rationals resp. over finite fields, and the idea of Shimoyama-Yokoyama resp. Eisenbud-Hunecke-Vasconcelos to extract primary ideals from pseudo-primary ideals. A parallelized version of the algorithm is implemented in Singular. Examples and timings are given at the end of the article.

We present an algorithm to compute the primary decomposition of a submodule N of the free module Z [x1, . . . , xn] m . For this purpose we use algorithms for primary decomposition of ideals in the polynomial ring over the integers. The idea is to compute first the minimal associated primes of N , i.e. the minimal associated primes of the ideal Ann . . , xn] and then compute the primary components using pseudo-primary decomposition and extraction, following the ideas of ShimoyamaYokoyama. The algorithms are implemented in Singular.

No abstract