Topological indices are the fixed numbers associated with the graphs. In recent years, mathematicians used indices to check the pharmacology characteristics and molecular behavior of medicines. In this article the first Zagreb connection number index is computed for the nanotubes VC5C7[ p, q] , HC5C7[ p,q] and Boron triangular Nanotubes. Also, the same index is computed for the Quadrilateral section $P_{m}^{n}$and $P_{m+\frac{1}{2}}^{n}$cuts from regular hexagonal lattices.

We find a class of block graphs whose binomial edge ideals have minimal regularity. As a consequence, we characterize the trees whose binomial edge ideals have minimal regularity. Also, we show that the binomial edge ideal of a block graph has the same depth as its initial ideal.

Topological indices have been computed for various molecular structures over many years. These are numerical invariants associated with molecular structures and are helpful in featuring many properties. Among these molecular descriptors, the eccentricity connectivity index has a dynamic role due to its ability of estimating pharmaceutical properties. In this article, eccentric connectivity, total eccentricity connectivity, augmented eccentric connectivity, first Zagreb eccentricity, modified eccentric connectivity, second Zagreb eccentricity, and the edge version of eccentric connectivity indices, are computed for the molecular graph of a PolyEThyleneAmidoAmine (PETAA) dendrimer. Moreover, the explicit representations of the polynomials associated with some of these indices are also computed.

Irregularity indices are usually used for quantitative characterization of the topological structures of non-regular graphs. In numerous problems and applications, especially in the fields of chemistry and material engineering, it is useful to be aware of the irregularity of a molecular structure. Furthermore, the evaluation of the irregularity of graphs is valuable not only for quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies but also for various physical and chemical properties, including entropy, enthalpy of vaporization, melting and boiling points, resistance, and toxicity. In this paper, we will restrict our attention to the computation and comparison of the irregularity measures of different classes of dendrimers. The four irregularity indices which we are going to investigate are σ irregularity index, the irregularity index by Albertson, the variance of vertex degrees, and the total irregularity index.

Colchicine, extracted from the colchicum autumnale plant, used by the ancient Greeks more than 20 centuries ago, is one of the most ancient drugs still prescribed even today. The major mechanism of action is binding to microtubules thereby interfering with mitosis and subsequent modulation of polymorphonuclear leukocyte function. Colchicine has long been of interest in the treatment of cardiovascular disease; however, its efficacy and safety profile for specific conditions have been variably established in the literature. In the subset of pericardial diseases, colchicine has been shown to be effective in recurrent pericarditis and post-pericardiotomy syndrome (PPS). The future course of treatment and management will therefore highly depend on the results of the ongoing large randomized placebo-controlled clinical trial to evaluate the efficacy and safety of colchicine for the primary prevention of several postoperative complications and in the perioperative period. Also, given the positive preliminary outcomes of colchicine usage in pericardial effusions, the future therapeutical use of colchicine looks promising. Further study is needed to clarify its role in these disease states, as well as explore other its role in other cardiovascular conditions.