Advances and Applications in Discrete Mathematics

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TOPOLOGICAL INDICES OF A CLUSTER OF TWO COMPLETE GRAPHS: A DEGREE-BASED APPROACH

Authors

  • R. Chitradevi
  • R. Senthil Amutha

Keywords:

Zagreb indices, hyper-Zagreb index, Sigma index, Sombor index, forgotten index, SK index, index, index, cluster graph

DOI:

https://doi.org/10.17654/0974165825038

Abstract

In this paper, we study some degree-based topological indices, such as, first Zagreb index $\left(M_1(G)\right)$, second Zagreb index $\left(M_2(G)\right)$, third Zagreb index $\left(M_3(G)\right)$, hyper-Zagreb index $(H M(G))$, sigma index $(\sigma(G))$, Sombor index $(S O(G))$, forgotten index $(F(G)), S K$ index, $S K_1$ index and $S K_2$ index of $K_m\left\{K_n\right\}$.

Received: November 26, 2024
Revised: May 2, 2025
Accepted: May 16, 2025

References

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[2] B. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015), 1184-1190.

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[4] G. H. Shirdel, H. Rezapour and A. M. Sayadi, The hyper Zagreb index of graph operations, Iranian Journal of Mathematical Chemistry 4 (2013), 213-220.

[5] I. Gutman and K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004), 83-90.

[6] I. Gutman, I. Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86 (2021), 11-16.

[7] I. Gutman, M. Togan, A. Yurttas, A. S. Cevik and I. N. Cangul, Inverse problem for Sigma index, MATCH Commun. Math. Comput. Chem. 79 (2018), 491-508.

[8] I. Gutman and N. Trinajstic, Graph theory and molecular orbitals. Total  electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), 535-538.

[9] G. Indulal and Dragan Stevanovic, The distance spectrum of corona and cluster of two graphs, AKCE Int. J. Graphs Comb. 12 (2015), 186-192.

[10] I. Naci Cangul, A. Yurttas, M. Togan and A. Sinan Cevik, Some formulae for the Zagreb indices of graphs, AIP Conference Proceedings 1479 (2012), 365-367.

[11] J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, Macmillan Press Ltd, New York, 1976.

[12] R. Frucht and F. Harary, On the corona of two graphs, Aequationes Math. 4 (1970), 322-325.

[13] V. Shigehalli and R. Kanabur, Computing degree-based topological indices of polyhex nanotubes, Journal of Mathematical Nanoscience 6 (2016), 47-55.

[14] V. S. Agnes and C. Kannadasan, Y-index of different corona products of graphs, Communications in Mathematics and Applications 14 (2023), 131-141.

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Published

2025-08-06

Issue

Vol. 42 No. 6 (2025)

Section

Articles

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How to Cite

TOPOLOGICAL INDICES OF A CLUSTER OF TWO COMPLETE GRAPHS: A DEGREE-BASED APPROACH. (2025). Advances and Applications in Discrete Mathematics, 42(6), 597-612. https://doi.org/10.17654/0974165825038

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