Computational Approaches to Connection Number-Based Indices in Metal-Organic Graphs

Abstract

Connection number–based topological indices play an important role in chemical graph theory by providing quantitative measures of structural characteristics in molecular and network-based systems. This thesis presents a comprehensive computational study of sev- eral connection number–based indices for metal–organic graphs and their associated line and praline´ graphs. Metal–organic networks are modeled as finite, simple, and connected graphs. For these graphs and their transformations, explicit computational expressions are developed for key connection number–based indices, including the first connection number index, second connection number index, connection number Zagreb indices, modified connection number indices, and selected degree–connection hybrid indices. Closed-form formulas are obtained in terms of fundamental graph parameters such as vertex degrees, connection numbers, and the number of edges. The effect of graph operations, particularly line graph and para line graph constructions, on the behavior of these indices is analyzed in detail. A comparative investigation high- lights how these transformations influence connectivity patterns and structural complex- ity in metal–organic graphs. The results indicate that connection number–based indices are effective in distinguishing structural variations and capturing topological properties of metal–organic networks. The findings of this thesis contribute to the theoretical advancement of connection num- ber–based topological indices and provide useful computational tools for the analysis and modeling of metal–organic structures in mathematical chemistry and related disciplines.