Suppose that $G$ is a connected graph constructed from pairwise disjoint connected graphs $G_1,\ldots ,G_t$ by selecting a vertex of $G_1$, a vertex of $G_2$, and identifying these two vertices. Then continue in this manner inductively. The graphs $G_1,\ldots ,G_k$ are the primary subgraphs of $G$. Some particular cases of these graphs are important in chemistry which we consider them in this paper and study their elliptic Sombor index.
1. S. Alikhani, N. Ghanbari, Sombor index of polymers, MATCH Commun. Math. Comput. Chem., 86, 715–728 (2021). 2. S. Alikhani, N. Ghanbari, M. A. Dehghanizadeh, Elliptic Sombor energy of a graph, submitted. Available at https://arxiv.org/abs/2404.18622. 3. S. Alikhani, M. A. Iranmanesh, Hosoya polynomial of dendrimer nanostar D3[n] MATCH Commun. Math. Comput. Chem. 71, 395–405 (2014). 4. M. Chellali, Bounds on the 2-domination number in cactus graphs, Opuscula Math. 2, 5–12 (2006). 5. K. C. Das, A. S. Cevik, I. N. Cangul, Y. Shang, On Sombor index, Symmetry 13, 140 (2021). 6. H. Deng, Z. Tang, R. Wu, Molecular trees with extremal values of Sombor indices, Int. J. Quantum Chem., 121, e26622 (2021). 7. M. V. Diudea, I. Gutman, J. Lorentz, Molecular Topology, Nova Science Publishers Huntington, NY, USA, (2001). 8. R. Cruz, I. Gutman, J. Rada, Sombor index of chemical graphs, Appl. Math. Comp., 399, 126018 (2021). 9. D. Emeric, S. Klavžar, Computing Hosoya polynomials of graphs from primary subgraphs, MATCH Commun. Math. Comput. Chem., 70, 627–644 (2013). 10. C. Espinal, I. Gutman, J. Rada, Elliptic Sombor index of chemical graphs, Commun.Comb. Optim., 1-11 (2024). 11. N. Ghanbari, On the Graovac-Ghorbani and atom-bond connectivity indices of graphs from primary subgraphs, Iran. J. Math. Chem., 13(1), 45–72 (2022). 12. N. Ghanbari, On the Sombor characteristic polynomial and Sombor energy of a graph, Comp. Appl. Math., 41, 242 (2022). 13. N. Ghanbari, S. Alikhani, Mostar index and edge Mostar index of polymers, Comp. Appl. Math., 40, 260 (2021). 14. N. Ghanbari, S. Alikhani, Sombor index of certain graphs, Iranian J. Math. Chem., 12(1), 27–37 (2021).
Ghanbari, N., & Alikhani, S. (2024). Elliptic Sombor Index of Graphs From Primary Subgraphs. Analytical and Numerical Solutions for Nonlinear Equations, 8(1), 99-109. doi: 10.22128/gadm.2024.842.1115
MLA
Nima Ghanbari; Saeid Alikhani. "Elliptic Sombor Index of Graphs From Primary Subgraphs", Analytical and Numerical Solutions for Nonlinear Equations, 8, 1, 2024, 99-109. doi: 10.22128/gadm.2024.842.1115
HARVARD
Ghanbari, N., Alikhani, S. (2024). 'Elliptic Sombor Index of Graphs From Primary Subgraphs', Analytical and Numerical Solutions for Nonlinear Equations, 8(1), pp. 99-109. doi: 10.22128/gadm.2024.842.1115
VANCOUVER
Ghanbari, N., Alikhani, S. Elliptic Sombor Index of Graphs From Primary Subgraphs. Analytical and Numerical Solutions for Nonlinear Equations, 2024; 8(1): 99-109. doi: 10.22128/gadm.2024.842.1115
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