journal-of-discrete-mathematical-sciences-and-cryptography Journal of Discrete Mathematical Sciences and Cryptography 2169-0065 0972-0529 Taru Publications 10.47974/JDMSC-2135 Graph Edge Hyper-Zagreb index : Applications and thermodynamic property predictions for linear acenes molecules Aliannejadi Zohreh Department of Mathematics, South Tehran Branch, Deh Haghi Street, Islamic Azad University, Pirouzi Street, Tehran, Iran Alamoti Somayeh Shafiee Department of Mathematics, South Tehran Branch, Deh Haghi Street, Islamic Azad University, Pirouzi Street, Tehran, Iran 29 1 49 64 26 02 2025

This research explores the Edge Hyper-Zagreb index, a unique method of calculating graph indices by replacing vertex degrees with edge degrees. The edge degree is obtained by summing the degrees of the end vertices and subtracting 2. We analyze the Edge Hyper-Zagreb index for the Cartesian product and join of graphs and compute it for linear Acenes molecules with the formula (C4n+2 H2n+4). Besides, we highlight the correlation between topological indices and the quantity of rings, using the Topological Indices Method (TIM) to predict the diverse thermodynamic characteristics of the Acenes family, like electron affinity, bond strength, heat of formation, and gap energy.

 Energy affinity of electrons Bonding energy Energy cap Formation heat energy Edge Hyper-Zagreb Graph index Linear acenes molecules access open retracted no