We examine degree-based topological co-indices in this paper for the network of titanium diboride \((TiB_2)\) and statistically analyze them. We examine complexity, connectedness, and stability in the network of \((TiB_2)\) using mathematical and computational techniques to identify important co-indices, such as ABC, GA, HM, and other polynomial-based indices. To determine the molecular and structural properties of materials, topological co-indices are needed. The paper emphasizes the relevance of these indices to materials science by examining deeper into correlations between them and the physical properties of \((TiB_2)\) . The network’s topological structure for titanium diboride can be better explained because of statistical distribution and numerical comparison among these indices. Our results promote computational material design by demonstrating the effectiveness of degree-based topological co-indices in predicting material behaviors.
