Early and correct classification of neurodegenerative diseases like Alzheimer's Disease (AD) and Frontotemporal Dementia (FTD) is one of the most important challenges in clinical neurology. In this paper, we present a novel electroencephalogram (EEG)-based approach that integrates a rich set of multiresolution features to improve the performance of automatic classification. Our approach fuses the Graph Fourier Transform (GFT), Graph Wavelet Transform (GWT), Discrete Wavelet Transform (DWT), and a newly developed Graph Empirical Mode Decomposition (GEMD) technique to primarily boost the performance of the proposed model. This also retained the complementary spatial, spectral, and temporal information carried by the EEG signals, which are significant for the differentiation of AD, FTD, and HC subjects. The EEG recordings were segmented into fixed lengths with non-overlapping windows of four durations: 1000, 5000, 10,000, and 20,000 samples. Energy and entropy features were obtained for each segment, both individually within domains and combined into a single 388-dimensional feature vector. The features were then normalized and fed into various machine learning (ML) models, including support vector machines (SVMs), k-nearest neighbors (kNNs), decision trees (DTs), random forests (RFs), and an ensemble learning model with the AdaBoost capability. The proposed model was tested using accuracy, precision, recall, specificity, and F1-scores, with results showing that the ensemble model was better than the other benchmark models in every classification task. That is, in this binary classification problem, an accuracy of 98.84% for AD vs. HC, 98.67% for AD vs. FTD, and 98.94% for FTD vs. HC was obtained. In the multiclass task (AD, FTD, HC), the method reached 96.68% accuracy, demonstrating the efficacy of the proposed method for the identification of Alzheimer's disease and frontotemporal dementia. Compared to previous research using the same dataset, our approach has demonstrated improved performance, validating the effectiveness of graph-based multiresolution feature fusion for dementia classification using EEG signals.