Chromatic indices of finite affine & projective planes and their duals

In this study, rather than transitioning directly from geometric structures to graph theory, we have derived several general results and theorems concerning the coloring of points and lines within affine and projective structures. We approached this topic through the lens of vertex and edge coloring concepts, pivotal subjects within graph theory. Our investigation sheds light on the intricate relationship between geometric structures and graph theory, providing a novel perspective on coloring methodologies. Extending the principles of vertex and edge coloring to affine and projective spaces, we uncover fundamental insights into the interplay between geometry and combinatorial mathematics.