In an attempt to analyse how the properties evolve with the cluster size, we report the results of a first principle density functional study on the electronic structures and properties of (BCN)$_x$ clusters (where x = 1 to 5) as well as (BCN)$_{12}$ nanotube. We have investigated geometries of (BCN)$_x$ and their isomers at the B3LYP/6-311G(d) level of theory and their vibrational as well as optical spectra. Their relative stability is discussed by calculating the binding energies. The electronic properties of (BCN)$_x$ clusters and the nanotube are analysed by the frontier orbitals and density of state curves. The frontier orbital energy gap of (BCN)$_{12}$ nanotube is found to be comparable to carbon nanotube but much small as compared to BN nanotube. Various electronic parameters of (BCN)$_x$ clusters have been calculated and their variation with the increase in x has been analysed. The study should be useful in the design of hybrid BCN-based nanostructures for possible applications analogous to purely carbon-based nanostructures.

In this paper, we have constructed a well-behaved, realistic and stable model for relativistic compact star in the presence of isotropic charged fluid by solving the Einstein–Maxwell field equations. To put the coupled differential equations into a closed system, we have employed the Vaidya and Tikekar (J. Astrophys. Astron.3:325, 1982) form of the metric potential g$_{rr}$ and assumed a completely new form of metric potential g$_{tt}$. The resulting energy–momentum components, i.e., energy density and pressure, contain six constants; two of these are determined through the boundary conditions. The remaining constants are constrained by physical requirements of a realistic compact star. The physical acceptability of the model is tested using the observational data of pulsar PSR B0943+10. Using graphical analysis, we have shown that this theoretical model obeys all the physical requirements and approximates observations of pulsar PSR B0943+10 to an excellent degree of accuracy. The stability of this model is evaluated using the Tolman–Oppenheimer–Volkoff equation, the adiabatic index and the Harrison–Zeldovich–Novikov criterion and it has passed the evaluation.