Context <p>Holey nanographene, an allotrope of carbon arranged in two dimensions, has gained remarkable attention as a nanomaterial with several potential uses in numerous industries, such as electronics, energy storage, healthcare, and environmental cleanup, because of its high carrier mobility, flexibility, transparency, high surface area, conductivity, and chemical stability. The fundamental holey nanographene is assembled in a linear form to create the holey nanographene chain (HNC) that is being discussed. To fully utilize it in various applications, it is essential to comprehend the basic ideas guiding its behavior at the nanoscale; for that, we find various topological indices for this holey nanographene chain using the cut method. Because topological indices are a robust mathematical tool that links molecular structure with chemical, physical, and biological properties, they are essential in diverse areas, namely chemistry, pharmaceutical research, environmental science, and materials science</p> Methods <p>The cut method is essential for calculating topological indices in large structures as standard definitions become increasingly complex for such computations. In this study, we apply the cut method to compute each topological index for holey nanographene structures, which involves extensive summations. MATLAB software is employed to simplify these calculations. To generate the DDSV (Distance Degree Sequence Vector) for each vertex within any dimension of holey nanographene, we utilize the NEWGRAPH interface. Python code is then used to analyze the DDSVs assigned to each vertex. Additionally, MATLAB code is applied to validate the numerical results derived from analytical formulae for the topological indices of the HNCs under consideration</p>