On Distance Energy of Graphs

The D-eigenvalues of a graph G are the eigenvalues of its distance matrix D, and the D-energy ED(G) is the sum of the absolute values of its D-eigenvalues. Two graphs are said to be D-equienergetic if they have the same D-energy. In this note we obtain bounds for the distance spectral radius and D-energy of graphs of diameter 2. Pairs of equiregular D-equienergetic graphs of diameter 2, on p = 3t + 1 vertices are also constructed.

Vibrational spectroscopic studies and computational study of quinoline-2-carbaldehyde benzoyl hydrazone

FT-IR spectrum of quinoline-2-carbaldehyde benzoyl hydrazone (HQb H2O) was recorded and analyzed. The synthesis and crystal structure data are also described. The vibrational wavenumbers were examined theoretically using the Gaussian03 package of programs using HF/6-31G(d) and B3LYP/6-31G(d) levels of theory. The data obtained from vibrational wavenumber calculations are used to assign vibrational bands obtained in infrared spectroscopy of the studied molecule. The first hyperpolarizability, infrared intensities and Raman activities are reported. The calculated first hyperpolarizability is comparable with the reported values of similar derivatives and is an attractive object for future studies of non-linear optics. The geometrical parameters of the title compound obtained from XRD studies are in agreement with the calculated values. The changes in the CAN bond lengths suggest an extended p-electron delocalization over quinoline and hydrazone moieties which is responsible for the non-linearity of the molecule