Leukemia is a malignant disease that impacts explicitly the blood cells, leading to life-threatening infections and premature mortality. State-of-the-art machine-enabled technologies and sophisticated deep learning algorithms can assist clinicians in early-stage disease diagnosis. This study introduces an advanced end-to-end approach for the automated diagnosis of acute leukemia classes acute lymphocytic leukemia (ALL) and acute myeloid leukemia (AML). This study gathered a complete database of 44 patients, comprising 670 ALL and AML images. The proposed deep model's architecture consisted of a fusion of graph theory and convolutional neural network (CNN), with six graph Conv layers and a Softmax layer. The proposed deep model achieved a classification accuracy of 99% and a kappa coefficient of 0.85 for ALL and AML classes. The suggested model was assessed in noisy conditions and demonstrated strong resilience. Specifically, the model's accuracy remained above 90%, even at a signal-to-noise ratio (SNR) of 0 dB. The proposed approach was evaluated against contemporary methodologies and research, demonstrating encouraging outcomes. According to this, the suggested deep model can serve as a tool for clinicians to identify specific forms of acute leukemia.