Single phase silver aluminum titanate (Ag1/2Al1/2)TiO3, later called AAT, nanoceramic powder (particle size 2 to 7.5 nm) was synthesized by a low-cost, green and reproducible tartaric acid gel process. X-ray, FT-IR, energy dispersive X-ray and high resolution transmission electron microscopy analyses were performed to ascertain the formation of AAT nanoceramics. X-ray diffraction data analysis indicated the formation of monoclinic structure having the space group P2/m(10). UV-Vis study revealed the surface plasmon resonance at 296 nm. Dielectric study revealed that AAT nanoceramics could be a suitable candidate for capacitor applications and meets the specifications for “Z7R” of Class I dielectrics of Electronic Industries Association. Complex impedance analyses suggested the dielectric relaxation to be of non-Debye type. To find a correlation between the response of the real system and idealized model circuit composed of discrete electrical components, the model fittings were performed using the impedance data. Electric modulus studies supported the hopping type of conduction in AAT. The correlated barrier hopping model was employed to successfully explain the mechanism of charge transport in AAT. The ac conductivity data were used to evaluate the density of states at Fermi level and minimum hopping length of the compound.
Topological indices play a very important role in the mathematical chemistry. The topological indices are numerical parameters of a graph. The degree sequence is obtained by considering the set of vertex degree of a graph. Graph operators are the ones which are used to obtain another broader graphs. This paper attempts to find degree sequence of vertex–F join operation of graphs for some standard graphs.