Sharp upper bounds on forgotten and SK indices of cactus graph

Alsinai, Ammar; Rehman, Hafiz Mutee ur; Manzoor, Yasir; Cancan, Murat; Taş, Ziyattin; Farahani, Moahmmad Reza

doi:10.1080/09720529.2022.2027605

Open Access Research Article

Sharp upper bounds on forgotten and SK indices of cactus graph

^*Ammar AlsinaiCorresponding authoraliiammar1985@gmail.comDepartment of Studies in Mathematics University of Mysore, Manasagangotri Mysuru 570006 Karnataka IndiaBhubansewar, Odisha, 752054, IndiaView full profile → , Hafiz Mutee ur Rehmanmutee.rehman@ue.edu.pkDepartment of Mathematics Division of Science and Technology University of Education Lahore PakistanView full profile → , Yasir Manzooryasir36402@gmail.comDepartment of Mathematics Division of Science and Technology University of Education Lahore PakistanView full profile → , Murat Cancanm _cencen@yahoo.com; m _cancan@yyu.edu.trFaculty of Education Van Yuzuncu Yıl University Zeve Campus Tuşba, 65080 Van TurkeyFaculty of Education Van Yuzuncu Yıl University Zeve CampusTuşba, Van, 65080, Turkey0000-0002-8606-2274View full profile → , Ziyattin Taşztas@bingol.edu.trDepartment of Mathematics Bingol University TurkeyView full profile → , Moahmmad Reza FarahaniMohammad_Farahani@mathdep.iust.ac.ir, Mrfarahani88@gmail.comDepartment of Mathematics Iran University of Science and Technology (IUST) Narmak Tehran 16844 IranNarmak, Tehran, 16844, IranView full profile →

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pp. 281–302Vol. 26Issue 1February 2021DOI: 10.1080/09720529.2022.2027605 Crossmark XML

Received:: 30 Nov 2021
Published Online:: 24 Feb 2022
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1543
Pages:: 281–302

Abstract

Sheehalli and Kanabur presented new forms of topological indices known as SK indices which have many applications in chemical graph theory towards QSPR/QSAR. A simple connected graph Γ is called a cactus graph if and only if any two cycles in the graph have no common edge. In this paper, we will explore and determine the sharp upper bounds of cactus graph using different versions of SK indices. We will also characterize the extremal properties for these indices due to many applications in pharmacology and medicinal chemistry.

Keywords

Topological index Chemical graph theory Cactus graph

Subject Classifications

Primary 05C3192E10

References

Liu, J.B., Nadeem, M.F., Siddiqui, H.M.A., Nazir, W. (2019). Computing metric dimension of certain families of toeplitz graphs. IEEE Access, 7, 126734-126741. https://doi.org/10.1109/ACCESS.2019.2938579 [Crossref], [Web of Science ®], [Google Scholar]
Raheem, A., Hasni, R., Javaid, M., Umar, M. A. (2020). On cordial related labeling of isomorphic copies of paths and subdivision of star. Journal of Discrete Mathematical Sciences and Cryptography, 23(7), 1381-1390. https://doi.org/10.1080/09720529.2019.1698802 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
Siddiqui, H M.A., Hayat, S., Khan, A., Imran, M., Razzaq, A., Liu, J.B. (2019). Resolvability and fault-tolerant resolvability structures of convexpolytopes. Theoretical Computer Science, 796, 114-128. https://doi.org/10.1016/j.tcs.2019.08.032 [Crossref], [Web of Science ®], [Google Scholar]
Zhang, F., Nazeer, S., Habib, M., Zia, T.J., Ren, Z. (2019). Radio Number for Generalized Petersen Graphs P(n,2). IEEE Access, 7, 142000-142008. https://doi.org/10.1109/ACCESS.2019.2943835 [Crossref], [Web of Science ®], [Google Scholar]
Rafiullah, M., Siddiqu, H.M.A., Ahmad, S. (2019). Resolvability of some convex polytopes. Utilitas Mathematica, 111, 309-323. [Web of Science ®], [Google Scholar]
Schenker, A., Mark L., Horst B., Abraham K. Clustering of web documents using a graph model. In Web Document Analysis: Challenges and Opportunities, 3-18. 2003. doi: https://doi.org/10.1142/9789812775375_0001 [Crossref], [Google Scholar]
Marx, D. (2004). Graph colouring problems and their applications in scheduling, Periodica Polytechnica Electrical Engineering, 48(1-2), 11-16. [Google Scholar]
Eswaramurthy, V.P. New algorithm for analyzing performance of neighbor-hood strategies in solving job shop scheduling problems. Journal of ScientificIndustrial Research, (2008). [Google Scholar]
Wiener, H. (1947). Structural determination of paraffin boiling points. Journalof the American chemical society, 69(1), 17-20. https://doi.org/10.1021/ja01193a005 [Crossref], [PubMed], [Web of Science ®], [Google Scholar]
Shigehalli, V.S., Kanabur, R. (2016). Computation of new degree-basedtopological indices of graphene. Journal of Mathematics, 2016. https://doi.org/10.1155/2016/4341919 [Crossref], [Google Scholar]
Gutman, I. (2011). Multiplicative Zagreb indices of trees. Bull. Soc. Math.Banja Luka, 18, 17-23. [Google Scholar]
Klavzar, S., Rajapakse, A., Gutman, I. (1996). The Szeged and the Wienerindex of graphs. Applied Mathematics Letters, 9(5), 45-49. doi: https://doi.org/10.1016/0893-9659(96)00071-7 [Crossref], [Web of Science ®], [Google Scholar]
Akhter, N., Jamil, M.K., Tomescu, I. (2016). Extremal first and second Zagreb indices of apex trees. Jangjeon Mathematical Society,78(4) [Google Scholar]
Wang, S., Wei, B. (2016). Multiplicative Zagreb indices of cacti. DiscreteMathematics, Algorithms and Applications, 8(03), 1650040. https://doi.org/10.1142/S1793830916500403

Views: 178Downloads: 6Citations: 2

[1] Liu, J.B., Nadeem, M.F., Siddiqui, H.M.A., Nazir, W. (2019). Computing metric dimension of certain families of toeplitz graphs. IEEE Access, 7, 126734-126741. https://doi.org/10.1109/ACCESS.2019.2938579 [Crossref], [Web of Science ®], [Google Scholar]

[2] Raheem, A., Hasni, R., Javaid, M., Umar, M. A. (2020). On cordial related labeling of isomorphic copies of paths and subdivision of star. Journal of Discrete Mathematical Sciences and Cryptography, 23(7), 1381-1390. https://doi.org/10.1080/09720529.2019.1698802 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]

[3] Siddiqui, H M.A., Hayat, S., Khan, A., Imran, M., Razzaq, A., Liu, J.B. (2019). Resolvability and fault-tolerant resolvability structures of convexpolytopes. Theoretical Computer Science, 796, 114-128. https://doi.org/10.1016/j.tcs.2019.08.032 [Crossref], [Web of Science ®], [Google Scholar]

[4] Zhang, F., Nazeer, S., Habib, M., Zia, T.J., Ren, Z. (2019). Radio Number for Generalized Petersen Graphs P(n,2). IEEE Access, 7, 142000-142008. https://doi.org/10.1109/ACCESS.2019.2943835 [Crossref], [Web of Science ®], [Google Scholar]

[5] Rafiullah, M., Siddiqu, H.M.A., Ahmad, S. (2019). Resolvability of some convex polytopes. Utilitas Mathematica, 111, 309-323. [Web of Science ®], [Google Scholar]

[6] Schenker, A., Mark L., Horst B., Abraham K. Clustering of web documents using a graph model. In Web Document Analysis: Challenges and Opportunities, 3-18. 2003. doi: https://doi.org/10.1142/9789812775375_0001 [Crossref], [Google Scholar]

[7] Marx, D. (2004). Graph colouring problems and their applications in scheduling, Periodica Polytechnica Electrical Engineering, 48(1-2), 11-16. [Google Scholar]

[8] Eswaramurthy, V.P. New algorithm for analyzing performance of neighbor-hood strategies in solving job shop scheduling problems. Journal of ScientificIndustrial Research, (2008). [Google Scholar]

[9] Wiener, H. (1947). Structural determination of paraffin boiling points. Journalof the American chemical society, 69(1), 17-20. https://doi.org/10.1021/ja01193a005 [Crossref], [PubMed], [Web of Science ®], [Google Scholar]

[10] Shigehalli, V.S., Kanabur, R. (2016). Computation of new degree-basedtopological indices of graphene. Journal of Mathematics, 2016. https://doi.org/10.1155/2016/4341919 [Crossref], [Google Scholar]

[11] Gutman, I. (2011). Multiplicative Zagreb indices of trees. Bull. Soc. Math.Banja Luka, 18, 17-23. [Google Scholar]

[12] Klavzar, S., Rajapakse, A., Gutman, I. (1996). The Szeged and the Wienerindex of graphs. Applied Mathematics Letters, 9(5), 45-49. doi: https://doi.org/10.1016/0893-9659(96)00071-7 [Crossref], [Web of Science ®], [Google Scholar]

[13] Akhter, N., Jamil, M.K., Tomescu, I. (2016). Extremal first and second Zagreb indices of apex trees. Jangjeon Mathematical Society,78(4) [Google Scholar]

[14] Wang, S., Wei, B. (2016). Multiplicative Zagreb indices of cacti. DiscreteMathematics, Algorithms and Applications, 8(03), 1650040. https://doi.org/10.1142/S1793830916500403

Journal of Discrete Mathematical Sciences and Cryptography

Sharp upper bounds on forgotten and SK indices of cactus graph

Abstract

Keywords

Subject Classifications

References