Character recognition using Graph Based Method technique the structural properties of characters by representing them as graphs, making it well-suited for recognizing characters with complex shapes and topologies. However, variations in handwriting styles and fonts pose significant challenges to the accuracy and reliability of these systems. This research investigates the robustness of graph-based character recognition to such variations, aiming to enhance its performance in real-world Research issues handwritten style Variation Character using Attributed relational graphs (ARGs).The study begins by analysing how different handwriting styles and font variations affect the graph representation of characters, identifying key factors that contribute to recognition errors. To address these challenges, we develop novel graph construction techniques that normalize and standardize character graphs, reducing sensitivity to stylistic differences. Additionally, we propose adaptive graph matching algorithms that allow for flexibility in handling discrepancies caused by variations in style and handwriting.The proposed methods are rigorously evaluated across diverse datasets, encompassing a wide range of handwriting styles, fonts, and noise levels. Our results demonstrate significant improvements in recognition accuracy and robustness, particularly in challenging scenarios with substantial variations in character appearance. The research not only advances the state of the art in graph-based character recognition but also provides valuable insights into the development of more resilient recognition systems that can generalize across different writing styles and fonts.This work has broad implications for applications such as digitizing handwritten documents, real-time handwriting recognition, and multilingual text processing, where robustness to style variations is essential.