COUNTING POLYNOMIALS AND ASSOCIATED TOPOLOGICAL INDICES OF NANOGRAPHENE AND TRIANGULAR NANOGRAPHENE WITH PENDANT EDGES: A PYTHON-BASED COMPUTATIONAL FRAMEWORK
P. Yakkana Rajasankar, S. Meenakshi
Department of Mathematics, Vels Institute of Science, Technology and Advanced Studies, Chennai – 600117, India
Abstract: In this paper, Nanographene with pendant edges and Triangular nanographene with pendant edges are investigated for general dimension using graph-theoretical methods. Edge distances are calculated by applying acute cuts, middle cuts, and pendant edge cuts. Based on these distances, derived four specific counting polynomials namely, the Omega, Theta, Pi, and Sadhana polynomials , and the subsequent indices are obtained for both classes of structures. These polynomials are examined in relation to their underlying physical structure, giving information on topological variation, electronic movement, and possible chemical uses. The theoretical knowledge of chemically significant nanostructures is improved by this work, which also creates opportunities for modeling their behavior using polynomial invariants. In addition, Python-based algorithms are proposed to generate the both structures for any dimension and to compute the associated polynomials and indices efficiently. The computational results are consistent with the theoretical findings, confirming the correctness of the approach. The proposed methodology enables rapid computation, producing results within a very short time, and gives an effective framework for analyzing nanographene structures with pendant edges.
Keywords: Nanographene, Triangular nanographene, Pendant edges, Graph polynomials, Omega polynomial, Theta polynomial, Pi polynomial and Sadhana polynomial, indices.
VOLUME 10 ISSUE 04 2026: 345 – 379