On connection number-based topological indices and entropy measures for triangular $$\gamma$$ -graphyne network

Triangular \(\gamma\)-graphyne has a special carbon–carbon bonding arrangement, which results in outstanding electrical characteristics. It is a potential material for semiconductors and conductors in nanoelectronic devices. The number of vertices at a distance of 2 from a vertex is known as the connection number (CN) of that vertex. In this paper, we computed Zagreb-type indices based on connection numbers. In order to give us a better knowledge of the structural properties of molecules or networks, these indices are calculated. Following the computation of these indices, we investigated their use in computing entropy, providing important new information about the thermodynamic characteristics and complexity of the understudied systems. We used Python language to find the Pearson correlation coefficient between indices and entropy and show its heat map.