Computation of topological descriptors and energy for graph-based binary codes
Rameez Raja, Samir Ahmad Wagay · Advances in Mathematics of Communications · 2024
We compute topological indices of a generic connected threshold graph using its binary generating code. We demonstrate that for each prime $ p $ and positive integer $ n $, a zero-divisor graph associated with a polynomial ring $ \mathbb{Z}_p[x]/(x^n) $ is a connected threshold graph and present its binary generating code. Additionally, we provide several families of graph-based binary codes (threshold graphs) exhibiting hyper-energetic characteristics. Finally, the existence of hypo-energetic graph generated by certain binary code is shown, with its energy lying between the energy of a zero-divisor graph associated with a ring $ \mathbb{Z}_{p^2} $ and that of a graph generated by a binary code of the type $ 01^{n-1} $, where $ n = p^2 $.