let $g$ be a finite group and let $gk(g)$ be the prime graph of $g$. we assume that $ngeqslant 5 $ is an odd number. in this paper, we show that the simple groups $b_n(3)$ and $c_n(3)$ are 2-recognizable by their prime graphs. as consequences of the result, the characterizability of the groups $b_n(3)$ and $c_n(3)$ by their spectra and by the set of orders of maximal abelian subgroups are obtai...

In natural product synthesis, the procurement of easily accessible starting materials is crucial. Chromenones and their subclass, coumarins, are a wide family small, oxygen-containing aromatic heterocycles. Phenylcoumarins offer particularly excellent point for diverse chemical space products, thus staring more complex products. Herein, we report an efficient synthesis 3-phenylcoumarin bearing ...

We investigate the question of whether any d-colorable simplicial d-polytope can be octahedralized, i.e., subdivided to a d-dimensional geometric cross-polytopal complex. give positive answer in dimension 3, with additional property that octahedralization introduces no new vertices on boundary polytope.