EN
Lower and Upper Bounds for Some Degree-Based Indices of Graphs
Abstract
Topological indices are mathematical measurements regarding the chemical structures of any simple finite graph. These are used for QSAR and QSPR studies. We get bounds for some degree based topological indices of a graph using solely the vertex degrees. We obtain upper and lower bounds for these indices and investigate for the complete graphs, path graphs and Fibonacci-sum graphs.
Keywords
References
- [1] X. Li and I. Gutman, Mathematical Aspects of Randic-Type Molecular Structure Descriptors, Mathematical Chemistry Monographs, 1(1), Faculty of Science, University of Kragujevac, Kragujevac, (2006).
- [2] H. Narumi and M. Katayama, Simple topological index. A newly devised index characterizing the topological nature of structural isomers of saturated hydrocarbons, Mem. Fac. Engin. Hokkaido Univ., 16 (1984), 209-214. $\href{https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/38010/1/16(3)_209-214.pdf}{\mbox{[Web]}} $
- [3] D. Vukicevic and M. Gasperov, Bond additive modeling 1.Adriatic indices, Croat. Chem. Acta, 83(3) (2010), 243-260. $ \href{chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=ee388e313c250ec065ed20ea9d45dbd58f9b8c65}{\mbox{[Web]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-78650489346&origin=resultslist&sort=plf-f&src=s&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Bond+Additive+Modeling+1.+Adriatic+Indices%22%29&sessionSearchId=2b3b881954449b5ab9e76e44896e2fdc}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000285799300001}{\mbox{[Web of Science]}} $
- [4] M. Bhanumathi and K.E.J. Rani, On multiplicative sum connectivity index, multiplicative Randic index and multiplicative harmonic index of some nanostar dendrimers, Int. J. Eng. Sci. Adv. Comput. Bio-Tech., 9(2) (2018), 52-67. $ \href{https://doi.org/10.26674/ijesacbt/2018/49410 }{\mbox{[CrossRef]}} $
- [5] I. Gutman and M. Ghorbani, Some properties of the Narumi–Katayama index, Appl. Math. Lett., 25(10) (2012), 1435–1438. $ \href{https://doi.org/10.1016/j.aml.2011.12.018}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-84862998776&origin=resultslist&sort=plf-f&src=s&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Some+properties+of+the+Narumi%E2%80%93Katayama+index%22%29&sessionSearchId=2b3b881954449b5ab9e76e44896e2fdc}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000306872400036}{\mbox{[Web of Science]}} $
- [6] M. Ghorbani, M. Songhori and I. Gutman, Modified Narumi – Katayama index, Kragujevac J. Sci., 34 (2012), 57–64. $\href{https://www.pmf.kg.ac.rs/KJS/images/volumes/vol34/kjs34ghorbanigutman57.pdf}{\mbox{[Web]}} $
- [7] K. Ch. Das, M. Matejic, E. Milovanovic and I. Milovanovic, Bounds for symmetric division deg index of graphs, Filomat, 33(3) (2019), 683-698. $ \href{https://doi.org/10.2298/FIL1903683D}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85077850354&origin=resultslist&sort=plf-f&src=s&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Bounds+for+symmetric+division+deg+index+of+graphs%22%29&sessionSearchId=2b3b881954449b5ab9e76e44896e2fdc&relpos=1}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000496191500003}{\mbox{[Web of Science]}} $
- [8] K. Fox, W. B. Kinnersley, D. McDonald, N. Orlow and G. J. Puleo, Spanning paths in Fibonacci-Sum graphs, Fib. Quart.,52(1) (2014), 46-49. $\href{chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://www.fq.math.ca/Papers1/52-1/FoxKinnersleyMcDonaldOrlowPuleo.pdf}{\mbox{[Web]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-84896976822&origin=resultslist&sort=plf-f&src=s&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Spanning+paths+in+Fibonacci-Sum+graphs%22%29&sessionSearchId=2b3b881954449b5ab9e76e44896e2fdc}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000217593600008}{\mbox{[Web of Science]}} $
Details
Primary Language
English
Subjects
Applied Mathematics (Other)
Journal Section
Research Article
Early Pub Date
March 28, 2025
Publication Date
March 31, 2025
Submission Date
September 25, 2023
Acceptance Date
December 31, 2024
Published in Issue
Year 2025 Volume: 8 Number: 1
APA
Özkan Kızılırmak, G., Sevgi, E., Büyükköse, Ş., & Cangül, İ. N. (2025). Lower and Upper Bounds for Some Degree-Based Indices of Graphs. Fundamental Journal of Mathematics and Applications, 8(1), 12-18. https://doi.org/10.33401/fujma.1366063
AMA
1.Özkan Kızılırmak G, Sevgi E, Büyükköse Ş, Cangül İN. Lower and Upper Bounds for Some Degree-Based Indices of Graphs. Fundam. J. Math. Appl. 2025;8(1):12-18. doi:10.33401/fujma.1366063
Chicago
Özkan Kızılırmak, Gül, Emre Sevgi, Şerife Büyükköse, and İsmail Naci Cangül. 2025. “Lower and Upper Bounds for Some Degree-Based Indices of Graphs”. Fundamental Journal of Mathematics and Applications 8 (1): 12-18. https://doi.org/10.33401/fujma.1366063.
EndNote
Özkan Kızılırmak G, Sevgi E, Büyükköse Ş, Cangül İN (March 1, 2025) Lower and Upper Bounds for Some Degree-Based Indices of Graphs. Fundamental Journal of Mathematics and Applications 8 1 12–18.
IEEE
[1]G. Özkan Kızılırmak, E. Sevgi, Ş. Büyükköse, and İ. N. Cangül, “Lower and Upper Bounds for Some Degree-Based Indices of Graphs”, Fundam. J. Math. Appl., vol. 8, no. 1, pp. 12–18, Mar. 2025, doi: 10.33401/fujma.1366063.
ISNAD
Özkan Kızılırmak, Gül - Sevgi, Emre - Büyükköse, Şerife - Cangül, İsmail Naci. “Lower and Upper Bounds for Some Degree-Based Indices of Graphs”. Fundamental Journal of Mathematics and Applications 8/1 (March 1, 2025): 12-18. https://doi.org/10.33401/fujma.1366063.
JAMA
1.Özkan Kızılırmak G, Sevgi E, Büyükköse Ş, Cangül İN. Lower and Upper Bounds for Some Degree-Based Indices of Graphs. Fundam. J. Math. Appl. 2025;8:12–18.
MLA
Özkan Kızılırmak, Gül, et al. “Lower and Upper Bounds for Some Degree-Based Indices of Graphs”. Fundamental Journal of Mathematics and Applications, vol. 8, no. 1, Mar. 2025, pp. 12-18, doi:10.33401/fujma.1366063.
Vancouver
1.Gül Özkan Kızılırmak, Emre Sevgi, Şerife Büyükköse, İsmail Naci Cangül. Lower and Upper Bounds for Some Degree-Based Indices of Graphs. Fundam. J. Math. Appl. 2025 Mar. 1;8(1):12-8. doi:10.33401/fujma.1366063
