###### Abstract
The application of photoautotrophic cultivation in the wastewater treatment process is less feasible due to the reduced light penetration caused by large wastewater volumes, particularly when handling dark-colored wastewater. Heterotrophic cultivation offers a cost-effective scalability in simple bioreactors with an enhanced productivity over photoautotrophic cultivation but faces certain drawbacks such as the species specificity, contamination risks, and increased substrate costs [22]. In contrast, mixotrophic cultivation can simultaneously assimilate organic carbon, nutrients, and CO\({}_{2}\) through combined respiration and photosynthesis, addressing the limitations of single-mode systems. When applied to wastewater treatment, mixotrophic cultivation effectively enhances the biomass production with reduced production costs and provides additional advantages such as a lower light requirement and simultaneous production of photosynthetic biocompounds (e.g., phycocyanin and carotenoids), which is not attainable in the heterotrophic cultivation mode [17; 23]. The performance of the microalgal wastewater treatment process depends critically on both the microalgae strain selection and wastewater characteristics. It is therefore crucial to optimize the treatment process to maximize the biomass productivity. Selecting an algal species with a rapid growth and high wastewater tolerance is critical for optimizing treatment efficiency [24]. Promising candidates like _Chorella_ and _Scenedesmus_ (_Chlorophyta_) demonstrate such traits, which is exemplified by _C. vulgaris_ achieving an 89.5% TN and 85.3% TP removal in undiluted anaerobic swine wastewater within open raceway systems [25]. Microalgae, as unicellular cell factories, only primarily utilize simple molecules like sugars, nitrogen compounds, and amino acids. Although most sources of wastewaters contain abundant dissolved organic matter suitable for bacterial assimilation, most remain inaccessible as carbon sources for microalgae-mediated nutrient removal [26; 27]. Hence, supplementing with suitable carbon sources may be an essential strategy to enhance the efficiency of the wastewater treatment process [28]. The supplementation of both inorganic and organic carbon sources can promote microalgae growth, shorten the cultivation cycle, and enhance biomass accumulation [29]. In this regard, using carbon-supplemented mixotrophic cultivation in wastewater may effectively increase the microalgal biomass, thereby enhancing the nutrient removal efficiency and promoting the simultaneous production of high-value products such as lipids. Numerous studies have shown that glucose, a simple sugar, serves as the most effective carbon source for microalgae cultivation [17], demonstrating an 85% assimilation efficiency in synthesizing oligosaccharides and polysaccharides [29; 30]. It provides a higher energy content (approximately 2.8 kJ mol\({}^{-1}\)) than other carbon sources like acetate (0.8 kJ mol\({}^{-1}\)). Also, glucose supplementation was found to enhance the _C. vulgaris_ cell size and improve starch and lipid accumulation [29]. This study aims to explore the effect of carbon supplementation on the biomass production, nutrient removal, and potential lipid production of the oleaginous microalgal strain _C. vulgaris_ FACHB-8 in anaerobically digested swine wastewater (ADSW). In our previous work, we have evaluated the excellent ability of this strain in ADSW treatment and potential lipid production [31]. Moreover, _C. vulgaris_ has been demonstrated to be viable in integrated systems for various types of wastewater treatment alongside a simultaneous lipid production [11; 32].Therefore, _C. vulgaris_ FACHB-8 was selected and used in this study. To our knowledge, limited studies have investigated the effect of nutrient supplementation in the wastewater cultivation medium on the microalgal biomass production and lipid yield. Therefore, in our study, FACHB-8 was cultured in wastewater supplemented with various kinds of carbon sources to select the optimal carbon source.