<p>The line graph <em>L(G) </em>of an undirected graph <em>G </em>represents the adjacencies between the edges of</p>

<p><em>G</em>. Iterated line graphs are defined recursively as <em>Lk(G) = L(Lk-1(G)) </em>for <em>k &ge; 1</em>. This dissertation investigates the behavior and evolution of classical structural properties and parameter values&mdash;such as order, size, maximum/minimum degree, chromatic number, clique number, and vertex/edge connectivity&mdash;under repeated line-graph operators. We characterize the limits of these behaviors based on the initial structural configurations of prolific graphs. Furthermore, we explore topological chemical indices within this operational framework, focus extensively on structural behaviors minimizing or preserving the Wiener index across iterations, and establish exact bounds and configurations for families of trees, caterpillars, lobsters, and generalized stars.</p>