Balanced rank distribution labeling of ladder graphs, complete graphs and complete bipartite graphs

A balanced rank distribution labeling of a graph G of order n is a new kind of vertex labeling from {1, 2, 3, ..., k}(n = 6, complete graphs K-n for n >= 3 and complete bipartite graphs K-n/2,K-n/2 for even n >= 4 have been investigated and obtained the results on balanced rank distribution number (brd(G)) for the given graphs as follows: (i) brd(L-n/2) = 3n - 15, for even n >= 12 (ii) brd(K-n ) = n, for n >= 3 (iii) brd(K-n/2,K-n/2) = n, for even n >=

Multiprocessing Substrates Enhanced Ta₂O₅/NiCo₂O₄ Spinel Nanocomposites for Effective Electro-/Photocatalytic and Toxicological Effects via the Caenorhabditis elegans Model

NiCo2O4 spinel composites decorated with metal oxides (Ta2O5), reduced graphene oxide (rGO), polyaminoanthraquinone (PAAQ), and layered double hydroxide hydrotalcite (HTs) were synthesized by the hydrothermal route. The synthesized composites were characterized using X-ray powder diffraction (XRD), Brunauer–Emmett–Teller (BET), high-resolution transmission electron microscopy (HR-TEM), and X-ray photoelectron spectroscopy (XPS) analyses for structural parameters such as surface area, morphology, chemical composition, etc. The production of oxygen by the water oxidation technique is the most suitable eco-friendly method, where rGO@Ta2O5/NiCo2O4 (RTNCO) showed an efficient oxygen evolution reaction (OER) performance under 1 M KOH electrolyte. Lower Tafel slope and overpotential values of 76 mV dec–1 and 315 mV, respectively, were calculated for RTNCO. The photocatalytic degradation efficiencies calculated were MB = 97.86%, RhB = 94.75%, and AP = 96% under UV light illumination within 120 min. The degraded dye solution was tested on mung bean (Vigna radiata) plants to determine the toxicity of the dye solution after 15 days, and the results showed good seed germination similar to that in water as the control. The synthesized materials exhibited better antibacterial activity against Bacillus cereus, Staphylococcus aureus, Pseudomonas aeruginosa, and Escherichia coli. Interestingly, the toxicological effects of the degraded dyes and drug solutions were effectively studied in the Caenorhabditis elegans model. The overall results revealed that the synthesized composites are promising for electro-/photocatalytic and biological applications