Keywords:-
Keywords:
Topological indices, join, Corona product, Sub-division vertex product, Graph operations
Article Content:-
Abstract
Graph operations are essential to developing advanced network structures from simple graphs. In [12] they defined two new variants of corona product and discovered their topological indices. In this Study, we extended the work and obtain the formulas of Y- Index and Redefined third Zagreb index for corona join product and Sub-division vertex join product of graphs
References:-
References
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2. Narasingh Deo, Graph theory with applications to engineering and computer science, (Prentice Hall of India, 1990).
3. A. Ilic, G. Yu, L. Feng “On the eccentric distance sum of Graphs” J.Math. Anal. Appl., vol. 381, 590-600, 2011.
4. I. Gutman, N. Trinajstic, Graph theory and molecular orbitals III Total electron energy bydrocarbons, Chem. Phys. Lett., 17(1972), 535-538.
5. J. Devillers, A. T. Balaban(Eds.), Topological Indices and Related Descriptors in QSAR and QSPR, Gordon and Breach, Amsterdam (1999).
6. M. Bilal, M. K. Jamil, M. Waheed, A. Alameri, Three topological indices of two new variants of graph products,
Mathematical Problems in Engineering, (2021), https://do.org/10.1155/2021/7724177
7. I. Gutman, K. C. Das, The First Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem., 50 (2004), 83-92.
8. Abdu Alameri, Noman AI- Naggar , Mahmoud AI-Rumaima Mohammed Alshara_, Y- index of some graph
operations.15,(2020),173-179
9. Gajendra pratap singh, Aparajita Borah, Sangram ray, AReview paper on corona product of graphs.19,(2020),
1047-1054.
10. N. De, S.M.A. Nayeem, A. Pal, Modified eccentric connectivity index and polynomial of corona product of graphs,Int.J. Compt. Appl. 132(9)(2015)1-5
11. P. Lu, Y. Miao, Spectra of the subdivision-vertex and subdivision-edge coronae Unpublished manuscript, Available at arXiv:1302.0457
12. X. Liu, P. Lu, Spectra of subdivision-vertex and subdivision-edge neighborhood coronae, Linear Algebra and Its Application. 438(8)(2013)3547-3559.
13. Wei Gao, Mohammad R. Farahani , The Redefined First, Second and Third Zagreb Indices of Titania Nanotubes TiO2[m,n]. 10 (2016)272-277
14. S. Bark, G. Sahoo, On the Laplacian spectra of some variants of corona , Linear Algebra and its Applications,
http://dx.doi.org/10.1016/j.1aa.2016.09.030.
15. M.Elisai, B. Taeri, Four new sums of graphs and their Wiener indices, Discrete Appl. Math. 157(2009)794-803
16. J. B. Babujee, S. Ramakrishnan, Topological indices and new graph structures, Applied mathematical sciences, Vol 6 N0.108, 2012 5383-5401.
17. Rao Tabish, Muhammad Kamran Jamil, Further Results on Topological Indices of Two Corona Variants of Graph Products., arXiv:2111.11006vl
2. Narasingh Deo, Graph theory with applications to engineering and computer science, (Prentice Hall of India, 1990).
3. A. Ilic, G. Yu, L. Feng “On the eccentric distance sum of Graphs” J.Math. Anal. Appl., vol. 381, 590-600, 2011.
4. I. Gutman, N. Trinajstic, Graph theory and molecular orbitals III Total electron energy bydrocarbons, Chem. Phys. Lett., 17(1972), 535-538.
5. J. Devillers, A. T. Balaban(Eds.), Topological Indices and Related Descriptors in QSAR and QSPR, Gordon and Breach, Amsterdam (1999).
6. M. Bilal, M. K. Jamil, M. Waheed, A. Alameri, Three topological indices of two new variants of graph products,
Mathematical Problems in Engineering, (2021), https://do.org/10.1155/2021/7724177
7. I. Gutman, K. C. Das, The First Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem., 50 (2004), 83-92.
8. Abdu Alameri, Noman AI- Naggar , Mahmoud AI-Rumaima Mohammed Alshara_, Y- index of some graph
operations.15,(2020),173-179
9. Gajendra pratap singh, Aparajita Borah, Sangram ray, AReview paper on corona product of graphs.19,(2020),
1047-1054.
10. N. De, S.M.A. Nayeem, A. Pal, Modified eccentric connectivity index and polynomial of corona product of graphs,Int.J. Compt. Appl. 132(9)(2015)1-5
11. P. Lu, Y. Miao, Spectra of the subdivision-vertex and subdivision-edge coronae Unpublished manuscript, Available at arXiv:1302.0457
12. X. Liu, P. Lu, Spectra of subdivision-vertex and subdivision-edge neighborhood coronae, Linear Algebra and Its Application. 438(8)(2013)3547-3559.
13. Wei Gao, Mohammad R. Farahani , The Redefined First, Second and Third Zagreb Indices of Titania Nanotubes TiO2[m,n]. 10 (2016)272-277
14. S. Bark, G. Sahoo, On the Laplacian spectra of some variants of corona , Linear Algebra and its Applications,
http://dx.doi.org/10.1016/j.1aa.2016.09.030.
15. M.Elisai, B. Taeri, Four new sums of graphs and their Wiener indices, Discrete Appl. Math. 157(2009)794-803
16. J. B. Babujee, S. Ramakrishnan, Topological indices and new graph structures, Applied mathematical sciences, Vol 6 N0.108, 2012 5383-5401.
17. Rao Tabish, Muhammad Kamran Jamil, Further Results on Topological Indices of Two Corona Variants of Graph Products., arXiv:2111.11006vl
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Durga, M., & Nagarajan, D. (2023). Two Topological Indices of Two New Variants of Graph Products. International Journal Of Mathematics And Computer Research, 11(8), 3704-3707. https://doi.org/10.47191/ijmcr/v11i8.11