Abstract A zero-sum flow is an assignment of nonzero integers to the edges such that the sum of the values of all edges incident with each vertex is zero, and we call it a zero-sum k-flow if the absolute values of edges are less than k. We recall the zero-sum flow number of G as the least integer k for which G admitting a zero sum k-flow. In this paper we gave complete zero-sum flow and zero sum numbers for Octagonal Grid and Generalized Prism.

Aluminium (Al) samples were nitrided in 13.56 MHz radiofrequency (RF) discharge of 70:30 vol.% Ar:N2 mixture at substrate temperature of 400 °C and RF power of 300 W for different fill pressures and treatment times. The nitrided samples were then characterized for their structural and mechanical properties using x-ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive x-ray spectroscopy (EDS), and Vickers micro hardness testing. XRD peaks (110), (111) and (200) of aluminium nitride (AlN) and their downshift confirmed the nitride formation together with nitrogen diffusion. The metastable cubic phase (c-AlN) shows texture growth and re-orientation dependent on fill pressure and treatment time. SEM micrographs showed the surface morphology with micro-pores. EDS results showed that the nitrogen content was significantly increased with nitriding time, along with the removal of oxides. Vickers hardness of the Al surface was increased more than thrice for 30 hours nitriding.