A complex fuzzy set (CFS) is a remarkable generalization of the fuzzy set in which membership function is restricted to take the values from the unit circle in the complex plane. A CFS is an efficient model to deal with uncertainties of human judgement in more comprehensive and logical way due to the presence of phase term. In this research article, we introduce the concept of competition graphs under complex fuzzy environment. Further, we present complex fuzzy k-competition graphs and p-competition complex fuzzy graphs. Moreover, we consider m-step complex fuzzy competition graphs, complex fuzzy neighborhood graphs (CFNGs), complex fuzzy economic competition graphs (CFECGs) and m-step complex fuzzy economic competition graphs with interesting properties. In addition, we describe an application in ecosystem of our proposed model. We also provide comparison of proposed competition graphs with existing graphs.

The synthesis of a photo-catalyst with a narrow bandgap and efficient capability to degrade contaminants in the presence of sunlight is currently challenging but exciting. In this work, an efficient photocatalytic ternary nanocomposite g-C₃N₄/Cu@CdS has been synthesized successfully by using the co-precipitation method. The synthesized composite was then characterized by SEM, XRD studies, EDX analysis, and ultra-violet-visible (UV-VIS) spectroscopy. The catalytic efficiency for the methylene blue (MB) dye and drug degradation (ciprofloxacin) was assessed by UV-visible absorption spectra. Gram-positive and Gram-negative bacteria were used to test the fabrication composite’s antibacterial properties. Various compositions (1%, 3%, 5%, 7%, and 9%) of/Cu@CdS nanocomposite (NCs) and 20%, 30%, 40%, 50%, and 60% of g-C₃N₄ NCs were prepared. Results reveal that 5%Cu@CdS and 40%g-C₃N₄5%Cu@CdS showed maximum antibacterial activity and photocatalytic degradation of dye and drug. The X-ray pattern showed no remarkable change in doped and pristine CdS nanoparticles (NPs). The efficient photocatalytic degradation activity of the fabricated ternary nanocomposite against MB dye and ciprofloxacin an antibiotic drug makes it a viable contender for solving environmental problems.