Classification of time series data plays a critical role across various domains, enabling pattern recognition and trend prediction. Traditional methods like Dynamic Time Warping (DTW) have been widely used to measure similarity between time series, but there are challenges related to computational complexity and sensitivity to noise. The conventional DTW approach, with its quadratic time complexity, can be inefficient for large datasets, and some implementations may struggle with noise and local variations. To overcome these limitations, a novel method called Graph-Theoretic Dynamic Time Warping (GT-DTW) is proposed. GT-DTW represents each time series as a graph, applies DTW on the graph representations and calculates the distances between different time series based on these graph representations. This approach provides a robust and computationally efficient method for time series classification, and experimental results show that GT-DTW provides better results when compared with conventional methods on the benchmark datasets from the UCR time series database. GT-DTW also demonstrates enhanced effectiveness in situations where time series share fundamental similarities, yet are affected by intricate transformations, noise, inconsistencies in length, and localized distortions.