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.
[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]}} $
[9] A. Arman, D.S. Gunderson and P.C. Li, Properties of the Fibonacci-sum graph, arXiv:1710.10303v1[math.CO] (2017). $ \href{http://dx.doi.org/10.48550/arXiv.1710.10303}{\mbox{[CrossRef]}} $
[10] D. Tasçi, G. Özkan Kizilirmak, E. Sevgi and Ş Büyükköse, The bounds for the largest eigenvalues of Fibonacci-sum and Lucas-sum graphs,
TWMS J. App. Eng. Math., 12(1) (2022), 367-371. $ \href{chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://belgelik.isikun.edu.tr/xmlui/bitstream/handle/iubelgelik/3414/vol.12.no.1-32.pdf?sequence=1&isAllowed=y}{\mbox{[Web]}}
\href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85123522161&origin=resultslist&sort=plf-f&src=s&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22The+bounds+for+the+largest+eigenvalues+of+Fibonacci-sum+and+Lucas-sum+graphs%22%29&sessionSearchId=2b3b881954449b5ab9e76e44896e2fdc}{\mbox{[Scopus]}}
\href{https://www.webofscience.com/wos/woscc/full-record/WOS:000739899800032}{\mbox{[Web of Science]}} $
[11] A.Y. Güneş, S. Delen, M. Demirci, A.S. Çevik and İ.N. Cangül, Fibonacci Graphs, Symmetry, 12(9) (2020), 1383. $ \href{https://doi.org/10.3390/sym12091383}{\mbox{[CrossRef]}}
\href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85090400401&origin=resultslist&sort=plf-f&src=s&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Fibonacci+Graphs%22%29&sessionSearchId=2b3b881954449b5ab9e76e44896e2fdc&relpos=11}{\mbox{[Scopus]}}
\href{https://www.webofscience.com/wos/woscc/full-record/WOS:000587623100001}{\mbox{[Web of Science]}} $
[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]}} $
[9] A. Arman, D.S. Gunderson and P.C. Li, Properties of the Fibonacci-sum graph, arXiv:1710.10303v1[math.CO] (2017). $ \href{http://dx.doi.org/10.48550/arXiv.1710.10303}{\mbox{[CrossRef]}} $
[10] D. Tasçi, G. Özkan Kizilirmak, E. Sevgi and Ş Büyükköse, The bounds for the largest eigenvalues of Fibonacci-sum and Lucas-sum graphs,
TWMS J. App. Eng. Math., 12(1) (2022), 367-371. $ \href{chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://belgelik.isikun.edu.tr/xmlui/bitstream/handle/iubelgelik/3414/vol.12.no.1-32.pdf?sequence=1&isAllowed=y}{\mbox{[Web]}}
\href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85123522161&origin=resultslist&sort=plf-f&src=s&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22The+bounds+for+the+largest+eigenvalues+of+Fibonacci-sum+and+Lucas-sum+graphs%22%29&sessionSearchId=2b3b881954449b5ab9e76e44896e2fdc}{\mbox{[Scopus]}}
\href{https://www.webofscience.com/wos/woscc/full-record/WOS:000739899800032}{\mbox{[Web of Science]}} $
[11] A.Y. Güneş, S. Delen, M. Demirci, A.S. Çevik and İ.N. Cangül, Fibonacci Graphs, Symmetry, 12(9) (2020), 1383. $ \href{https://doi.org/10.3390/sym12091383}{\mbox{[CrossRef]}}
\href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85090400401&origin=resultslist&sort=plf-f&src=s&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Fibonacci+Graphs%22%29&sessionSearchId=2b3b881954449b5ab9e76e44896e2fdc&relpos=11}{\mbox{[Scopus]}}
\href{https://www.webofscience.com/wos/woscc/full-record/WOS:000587623100001}{\mbox{[Web of Science]}} $
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
Özkan Kızılırmak G, Sevgi E, Büyükköse Ş, Cangül İN. Lower and Upper Bounds for Some Degree-Based Indices of Graphs. Fundam. J. Math. Appl. March 2025;8(1):12-18. doi:10.33401/fujma.1366063
Chicago
Özkan Kızılırmak, Gül, Emre Sevgi, Şerife Büyükköse, and İsmail Naci Cangül. “Lower and Upper Bounds for Some Degree-Based Indices of Graphs”. Fundamental Journal of Mathematics and Applications 8, no. 1 (March 2025): 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
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, 2025, doi: 10.33401/fujma.1366063.
ISNAD
Özkan Kızılırmak, Gül et al. “Lower and Upper Bounds for Some Degree-Based Indices of Graphs”. Fundamental Journal of Mathematics and Applications 8/1 (March 2025), 12-18. https://doi.org/10.33401/fujma.1366063.
JAMA
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, 2025, pp. 12-18, doi:10.33401/fujma.1366063.
Vancouver
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):12-8.